C₃₇×#2578 #17991396

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#2578

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₇
prime radical	C₂²×D₄×C₃₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ G

468 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 generators on 61 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)(38,39,42,41)(40,44,45,43)(46,47)(48,52)(49,53)(50,51)(54,55)(56,60)(57,59)(58,61);(40,45)(43,44)(47,51)(48,53)(54,55,57,59)(56,58,61,60);(38,40)(39,43)(41,44)(42,45)(46,48)(47,49)(50,53)(51,52)(54,55)(56,58)(57,59)(60,61);(38,41,42,39)(40,44,45,43)(46,49)(47,48)(50,52)(51,53)(54,56,57,61)(55,58,59,60)

Conjugacy classes & character table

1406 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃₇×#2578, C₃₇×#34849, C₃₇×#34863, …
maximal normal subgroup of	C₂×C₃₇×#2578, C₃₇×#34849, C₃₇×#34863, …
maximal quotient of	C₃₇×#13919, C₃₇×#13947, C₃₇×#13988, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1310);

C37×#2578 #17991396