C₃₇×#3010 #17991828

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

Aliases

direct product

C₃₇×#3010

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

732 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)(43,47)(45,52)(48,54)(49,53)(51,56)(55,57);(42,43,46,49)(44,48,50,55)(45,53,52,47)(51,57,56,54);(39,41)(42,44)(43,48)(45,51)(46,50)(47,54)(49,55)(52,56)(53,57);(44,50)(48,55)(51,56)(54,57)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#13098, C₃₇×#13103, C₃₇×#23894, …
maximal normal subgroup of	C₃₇×#13098, C₃₇×#13103, C₃₇×#23894, …
maximal quotient of	C₃₇×#18226, C₃₇×#18234, C₃₇×#18242, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1742);

C37×#3010 #17991828