C₃₇×#3486 #17992304

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

Aliases

direct product

C₃₇×#3486

Subgroups

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

1492 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)(43,47)(45,53)(48,50)(51,57);(42,43,46,47)(44,50,52,48)(45,49,53,54)(51,56,57,55);(38,39)(40,41);(42,44,46,52)(43,48,47,50)(45,51,53,57)(49,55,54,56);(42,45)(43,49)(44,51)(46,53)(47,54)(48,55)(50,56)(52,57)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#8455, C₃₇×#12710, C₃₇×#12712, …
maximal normal subgroup of	C₃₇×#8455, C₃₇×#12710, C₃₇×#12712, …
maximal quotient of	C₃₇×#34173, C₃₇×#34200, C₃₇×#34249, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2218);

C37×#3486 #17992304