C₃₇×#3154 #17991972

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3057
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₃₇×#3154

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 ◁ #117×C₃₇ ◁ G

564 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)(39,41)(43,47)(45,52)(48,53)(49,54)(51,56)(55,57);(42,43,45,47,46,49,52,54)(44,48,51,53,50,55,56,57);(38,39,40,41)(42,44)(43,48)(45,51)(46,50)(47,53)(49,55)(52,56)(54,57);(44,50)(48,55)(51,56)(53,57)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#22284, C₃₇×#25440, C₃₇×#25443, …
maximal normal subgroup of	C₃₇×#22284, C₃₇×#25440, C₃₇×#25443, …
maximal quotient of	C₃₇×#19621, C₃₇×#19622, C₃₇×#19625, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1886);

C37×#3154 #17991972