C₃₇×#2475 #17991293

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#2475

Subgroups

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

476 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 2368

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

Conjugacy classes & character table

1406 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃₇×#2475, C₃₇×#34720, C₃₇×#34735, …
maximal normal subgroup of	C₂×C₃₇×#2475, C₃₇×#34720, C₃₇×#34735, …
maximal quotient of	C₃₇×#13897, C₃₇×#13944, C₃₇×#13986, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1207);

C37×#2475 #17991293