C₃₇×#3489 #17992307

order	4736
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₃₇×#3489

Subgroups

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

1522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 5 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)(42,43,47,48)(44,50,52,45)(46,54,55,49)(51,53,57,56);(43,48)(45,50)(49,54)(53,56);(38,39)(40,41)(42,44)(43,45)(46,51)(47,52)(48,50)(49,53)(54,56)(55,57);(42,45)(43,44)(46,53)(47,50)(48,52)(49,51)(54,57)(55,56);(42,46,47,55)(43,49,48,54)(44,51,52,57)(45,53,50,56)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#8467, C₃₇×#17606, C₃₇×#17608, …
maximal normal subgroup of	C₃₇×#8467, C₃₇×#17606, C₃₇×#17608, …
maximal quotient of	C₃₇×#34175, C₃₇×#34202, C₃₇×#34203, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2221);

C37×#3489 #17992307