C₃₇×#3012 #17991830

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3008
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₃₇×#3012

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 ◁ C₂×#41×C₃₇ ◁ G

764 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)(44,49)(45,50)(46,55)(47,51)(48,52)(53,56)(54,57);(42,44)(43,48)(45,52)(46,54)(47,53)(49,55)(50,56)(51,57);(39,41)(42,44)(43,49)(45,54)(46,52)(47,53)(48,55)(50,57)(51,56);(42,45,47,46)(43,50,51,55)(44,52,53,54)(48,56,57,49)

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#23886, C₃₇×#23888, C₃₇×#23889, …
maximal normal subgroup of	C₃₇×#23886, C₃₇×#23888, C₃₇×#23889, …
maximal quotient of	C₃₇×#18228, C₃₇×#18231, C₃₇×#18236, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1744);

C37×#3012 #17991830