C₃₇×#1733 #17990551

order	4736
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#1733

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₇	C₂×D₄
commutator	C₄	C₂×C₄²×C₃₇
Frattini, cosocle	C₂²×C₄	C₂³×C₃₇
socle	C₂²×C₃₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₃₇	D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ C₂³×C₄×C₃₇ ◁ G

404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(44,50)(45,53)(46,49)(47,52)(48,54)(51,56)(55,57);(42,44)(43,47,49,55)(45,52)(46,51)(48,50,53,56)(54,57);(44,51)(47,55)(50,56)(52,57)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#10740, C₃₇×#10741, C₃₇×#10743, …
maximal normal subgroup of	C₃₇×#10740, C₃₇×#10741, C₃₇×#10743, …
maximal quotient of	C₃₇×#7866, C₃₇×#7868, C₃₇×#7869, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 465);

C37×#1733 #17990551