C₃₇×#3005 #17991823

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₃₇×#3005

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 ◁ C₂³×C₄×C₃₇ ◁ G

758 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)(46,54)(47,50)(48,52)(53,56)(55,57);(42,44)(43,48)(45,52)(46,55)(47,53)(49,56)(50,57)(51,54);(39,41)(42,45,47,46)(43,49,50,54)(44,52,53,55)(48,56,57,51);(43,50)(48,57)(49,54)(51,56)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#23878, C₃₇×#23881, C₃₇×#23883, …
maximal normal subgroup of	C₃₇×#23878, C₃₇×#23881, C₃₇×#23883, …
maximal quotient of	C₃₇×#18134, C₃₇×#18139, C₃₇×#18144, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1737);

C37×#3005 #17991823