C₃₇×#3050 #17991868

order	4736
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#3050

Subgroups

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

520 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)(44,51)(45,49)(46,55)(47,50)(48,53)(52,56)(54,57);(42,44,46,53,47,54,45,52)(43,48,49,51,50,56,55,57);(39,41);(42,45,47,46)(43,49,50,55)(44,52,54,53)(48,51,56,57)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#11703, C₃₇×#11704, C₃₇×#11709, …
maximal normal subgroup of	C₃₇×#11703, C₃₇×#11704, C₃₇×#11709, …
maximal quotient of	C₃₇×#19101, C₃₇×#19105, C₃₇×#19110, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1782);

C37×#3050 #17991868