C₃₇×#3155 #17991973

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×#3155

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

596 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)(45,48)(49,53)(50,54)(52,55)(56,57);(42,43,48,54,46,50,45,47)(44,49,55,57,51,56,52,53);(38,39,40,41)(42,44)(43,49)(45,52)(46,51)(47,53)(48,55)(50,56)(54,57);(44,51)(49,56)(52,55)(53,57)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#13215, C₃₇×#13334, C₃₇×#13336, …
maximal normal subgroup of	C₃₇×#13215, C₃₇×#13334, C₃₇×#13336, …
maximal quotient of	C₃₇×#19623, C₃₇×#19627, C₃₇×#19629, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1887);

C37×#3155 #17991973