C₃₇×#3040 #17991858

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#3040

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₂×AGL(1,ℤ/8)×C₃₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

500 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)(39,41)(42,43)(44,52)(45,51)(46,48)(47,50)(49,53)(54,57)(55,56);(38,39,40,41)(43,48)(49,56)(50,51)(52,57);(42,44)(43,49)(45,53)(46,54)(47,55)(48,56)(50,52)(51,57);(42,45,46,47)(43,50,48,51)(44,53,54,55)(49,52,56,57)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#9349, C₃₇×#9350, C₃₇×#24473, …
maximal normal subgroup of	C₃₇×#9349, C₃₇×#9350, C₃₇×#24473, …
maximal quotient of	C₃₇×#19274, C₃₇×#19275, C₃₇×#19276, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1772);

C37×#3040 #17991858