C₃₇×#1446 #17990264

order	4736
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₃₇×#1446

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₃₇	C₂³
commutator	C₂³	C₂²×C₄×C₃₇
Frattini, cosocle	C₂⁴	C₂³×C₃₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₇ ◁ G

736 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 3 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)(42,43,44,45)(47,49);(46,47)(48,49)(50,51,53,55)(52,56,57,54);(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,52,53,57)(51,54,55,56)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#7131, C₃₇×#7308, C₃₇×#8455, …
maximal normal subgroup of	C₃₇×#7131, C₃₇×#7308, C₃₇×#8455, …
maximal quotient of	C₃₇×#7557, C₃₇×#11380, C₃₇×#11381, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 178);

C37×#1446 #17990264