C₃₇×#3284 #17992102

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×#3284

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

494 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)(42,43,48,45)(44,52,55,57)(46,51,47,50)(49,56,53,54);(42,44,48,55)(43,49,45,53)(46,54,47,56)(50,52,51,57);(39,41)(42,45,48,43)(44,53,55,49)(46,51,47,50)(52,54,57,56);(42,46)(43,50)(45,51)(47,48)(52,57)(54,56)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#19759, C₃₇×#19760, C₃₇×#19767, …
maximal normal subgroup of	C₃₇×#19759, C₃₇×#19760, C₃₇×#19767, …
maximal quotient of	C₃₇×#19851, C₃₇×#19852, C₃₇×#19853, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2016);

C37×#3284 #17992102