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Size rank n

Invariants Bases Automorphisms Dimension of realization space Girth Expected dimension over ℤ

Realizability realizable in char 0 realizable in characteristic char set class birational type

Properties Simple Connected Paving Uniform Regular Binary Ternary Quaternary Graphic Transversal Series parallel Self dual Orientable Supersolvable Three lines Free realization space Realization space: smooth over ℤ Realization space: is regular scheme

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32,400,859 matroids, showing 3,551–3,600

label ▲	rank ⇅	n ⇅	#bases ⇅	#automorphisms ⇅	simple ⇅	char set ⇅	rs dim ⇅	birational type ⇅
3.10.1644	3	10	110	1	✓	all but 2,3	0	rational
3.10.1645	3	10	110	2	✓	all but 2,3,5	0	rational
3.10.1646	3	10	112	8	✓	all but 2	1	rational
3.10.1647	3	10	111	8	✓	all but 2	0	rational
3.10.1648	3	10	111	4	✓	all but 2	1	rational
3.10.1649	3	10	110	8	✓	all but 2	0	rational
3.10.1650	3	10	111	1	✓	all but 2	2	rational
3.10.1651	3	10	110	1	✓	all but 2	1	rational
3.10.1652	3	10	110	1	✓	all but 2,5	0	rational
3.10.1653	3	10	110	2	✓	{5}	-1	rational
3.10.1654	3	10	111	24	✓	∅	-1	rational
3.10.1655	3	10	110	24	✓	{2}	-1	rational
3.10.1656	3	10	111	2	✓	{2}	-1	rational
3.10.1657	3	10	110	1	✓	{2}	-1	rational
3.10.1658	3	10	109	2	✓	∅	-1	rational
3.10.1659	3	10	110	1	✓	∅	-1	rational
3.10.1660	3	10	109	1	✓	all but 2	6	rational
3.10.1661	3	10	109	2	✓	all	6	empty
3.10.1662	3	10	110	1	✓	all but 2	5	rational
3.10.1663	3	10	109	1	✓	all but 2	5	rational
3.10.1664	3	10	109	2	✓	all but 2	4	rational
3.10.1665	3	10	110	1	✓	all but 2	3	rational
3.10.1666	3	10	109	1	✓	all but 2	5	rational
3.10.1667	3	10	109	1	✓	all but 2	4	rational
3.10.1668	3	10	109	1	✓	all but 2	3	rational
3.10.1669	3	10	110	2	✓	all but 2	4	rational
3.10.1670	3	10	109	2	✓	all	5	empty
3.10.1671	3	10	108	6	✓	all but 2	3	rational
3.10.1672	3	10	109	1	✓	all but 2	3	rational
3.10.1673	3	10	108	3	✓	all but 2	3	point over Q(a)/(a^2 - a - 1)
3.10.1674	3	10	108	2	✓	all	5	empty
3.10.1675	3	10	113	1008	✓	all but 2	5	empty
3.10.1676	3	10	112	1008	✓	all but 2	4	empty
3.10.1677	3	10	112	48	✓	all but 2	4	empty
3.10.1678	3	10	111	8	✓	all but 2	4	empty
3.10.1679	3	10	110	6	✓	all but 2	4	empty
3.10.1680	3	10	110	24	✓	all but 2	4	empty
3.10.1681	3	10	112	80640	✗	all	2	rational
3.10.1682	3	10	111	1440	✗	all	2	rational
3.10.1683	3	10	110	288	✗	all	3	rational
3.10.1684	3	10	110	96	✗	all	4	rational
3.10.1685	3	10	109	96	✗	all	2	rational
3.10.1686	3	10	109	16	✗	all	4	rational
3.10.1687	3	10	108	16	✗	all	1	rational
3.10.1688	3	10	109	96	✗	all	2	rational
3.10.1689	3	10	109	24	✗	all	3	rational
3.10.1690	3	10	108	8	✗	all	1	rational
3.10.1691	3	10	108	8	✗	all	3	rational
3.10.1692	3	10	108	8	✗	all	3	rational
3.10.1693	3	10	107	8	✗	all	2	rational