C₃₇×#2993 #17991811

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#2993

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₇	C₂⁴
commutator	C₂²	C₂³×C₄×C₃₇
Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
socle	C₂²×C₃₇	C₂³×C₄
prime radical	#121×C₃₇	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ G

354 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)(39,42)(40,44)(46,47,49,53,50,52,56,59)(48,51,55,58,54,57,60,61);(38,39)(40,43)(41,42)(44,45)(46,48)(47,51)(49,55)(50,54)(52,57)(53,58)(56,60)(59,61);(39,42)(43,45)(47,52)(51,57)(53,59)(58,61);(38,40,41,44)(39,43,42,45)(48,54)(51,57)(55,60)(58,61)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#17918, C₃₇×#17919, C₃₇×#17926, …
maximal normal subgroup of	C₃₇×#17918, C₃₇×#17919, C₃₇×#17926, …
maximal quotient of	C₃₇×#20548, C₃₇×#20553, C₃₇×#20561, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1725);

C37×#2993 #17991811