C₃₇×#3273 #17992091

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3264
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#3273

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₄×D₄×C₃₇ ◁ G

520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 4 generators on 57 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)(40,41)(42,43,46,49)(44,50,51,57)(45,54,55,48)(47,52,56,53);(42,44)(43,47)(45,52)(46,51)(48,57)(49,56)(50,54)(53,55);(39,41)(44,51)(47,56)(50,57)(52,53);(44,52)(45,55)(47,57)(48,54)(50,56)(51,53)

Conjugacy classes & character table

1073 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#12324, C₃₇×#12326, C₃₇×#12376, …
maximal normal subgroup of	C₃₇×#12324, C₃₇×#12326, C₃₇×#12376, …
maximal quotient of	C₃₇×#19884, C₃₇×#19891, C₃₇×#19899, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2005);

C37×#3273 #17992091