C₃₇×#2862 #17991680

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₃₇×#2862

Subgroups

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

504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7662, C₃₇×#7682, C₃₇×#7702, …
maximal normal subgroup of	C₃₇×#7662, C₃₇×#7682, C₃₇×#7702, …
maximal quotient of	C₃₇×#14687, C₃₇×#14703, C₃₇×#14707, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1594);

C37×#2862 #17991680