C₃₇×#3285 #17992103

order	4736
nilpotency class	3
isoclinism	isoclinic class of D₄×D₈
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#3285

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 ◁ C₄×D₄×C₃₇ ◁ G

482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 2368

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

Conjugacy classes & character table

1295 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#33831, C₃₇×#33835, C₃₇×#33836, …
maximal normal subgroup of	C₃₇×#33831, C₃₇×#33835, C₃₇×#33836, …
maximal quotient of	C₃₇×#19835, C₃₇×#19836, C₃₇×#19837, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2017);

C37×#3285 #17992103