C₃₇×#2716 #17991534

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#2716

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

450 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)(43,46)(44,48)(50,51,55,57)(52,54,53,56);(39,41)(43,46)(47,49)(50,52,55,53)(51,56,57,54);(38,39)(40,41)(42,43,45,46)(44,47,48,49)(50,53,55,52)(51,56,57,54);(42,44)(43,47)(45,48)(46,49)(50,54,55,56)(51,52,57,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#36742, C₃₇×#36745, C₃₇×#36760, …
maximal normal subgroup of	C₃₇×#36742, C₃₇×#36745, C₃₇×#36760, …
maximal quotient of	C₃₇×#14380, C₃₇×#14390, C₃₇×#14413, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1448);

C37×#2716 #17991534