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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 4,851–4,900

label ▼	rank ⇅	n ⇅	#bases ⇅	#automorphisms ⇅	simple ⇅	char set ⇅	rs dim ⇅	birational type ⇅
4.9.185363	4	9	109	32	✓	all	2	rational
4.9.185362	4	9	102	288	✓	all but 2	1	rational
4.9.185361	4	9	106	288	✓	all	3	rational
4.9.185360	4	9	107	12	✓	all	3	rational
4.9.185359	4	9	108	36	✓	all	3	rational
4.9.185358	4	9	107	6	✓	all but 2	2	rational
4.9.185357	4	9	108	12	✓	all	4	rational
4.9.185356	4	9	107	2	✓	all	2	rational
4.9.185355	4	9	108	4	✓	all	3	rational
4.9.185354	4	9	107	4	✓	all but 2	3	rational
4.9.185353	4	9	108	4	✓	all	3	rational
4.9.185352	4	9	108	4	✓	all	3	rational
4.9.185351	4	9	109	12	✓	all	4	rational
4.9.185350	4	9	108	48	✓	all	4	rational
4.9.185349	4	9	108	8	✓	all	0	rational
4.9.185348	4	9	109	16	✓	all	3	rational
4.9.185347	4	9	109	24	✓	all	1	rational
4.9.185346	4	9	110	96	✓	all	1	rational
4.9.185345	4	9	105	4320	✓	all	4	rational
4.9.185344	4	9	110	720	✓	all but 2,3	2	rational
4.9.185343	4	9	111	4320	✓	all	2	rational
4.9.185342	4	9	35	10080	✗	all	3	rational
4.9.185341	4	9	52	96	✗	∅	-1	rational
4.9.185340	4	9	53	32	✗	all	1	rational
4.9.185339	4	9	54	96	✗	∅	-1	rational
4.9.185338	4	9	55	1440	✗	all	4	rational
4.9.185337	4	9	70	720	✗	∅	-1	rational
4.9.185336	4	9	72	288	✗	all	2	rational
4.9.185335	4	9	73	96	✗	all but 2,3	0	rational
4.9.185334	4	9	74	288	✗	∅	-1	rational
4.9.185333	4	9	75	4320	✗	all	4	rational
4.9.185332	4	9	57	24	✗	∅	-1	rational
4.9.185331	4	9	58	8	✗	all	1	rational
4.9.185330	4	9	59	16	✗	all	4	rational
4.9.185329	4	9	60	144	✗	all	3	rational
4.9.185328	4	9	58	24	✗	all	4	empty
4.9.185327	4	9	59	24	✗	all	1	empty
4.9.185326	4	9	59	2	✗	all	2	rational
4.9.185325	4	9	59	4	✗	all	2	rational
4.9.185324	4	9	60	4	✗	all	2	rational
4.9.185323	4	9	59	2	✗	all	1	rational
4.9.185322	4	9	60	2	✗	∅	-1	rational
4.9.185321	4	9	60	1	✗	all	2	rational
4.9.185320	4	9	60	2	✗	all	1	rational
4.9.185319	4	9	61	2	✗	all but 2	1	rational
4.9.185318	4	9	60	2	✗	all	2	rational
4.9.185317	4	9	59	6	✗	all	5	rational
4.9.185316	4	9	60	1	✗	all	4	rational
4.9.185315	4	9	61	1	✗	all	1	rational
4.9.185314	4	9	61	6	✗	all	3	rational