C₃₇×#2626 #17991444

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₃₇×#2626

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₇
prime radical	C₂⁵×C₃₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ G

668 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)(42,43)(44,47)(45,46)(48,49)(50,51,54,55)(52,56,57,53);(39,41)(43,46)(47,48)(51,55)(52,57);(38,39)(40,41)(42,43)(44,48)(45,46)(47,49)(50,52,54,57)(51,53,55,56);(42,44)(43,47)(45,49)(46,48)(50,53)(51,52)(54,56)(55,57)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#9199, C₃₇×#9201, C₃₇×#9922, …
maximal normal subgroup of	C₃₇×#9199, C₃₇×#9201, C₃₇×#9922, …
maximal quotient of	C₃₇×#14262, C₃₇×#14265, C₃₇×#14275, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1358);

C37×#2626 #17991444