C₃₇×#3044 #17991862

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3008
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#3044

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₂×#41×C₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ #117×C₃₇ ◁ G

458 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 generators on 73 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)(42,43,47,51)(44,48,53,62)(45,55,57,65)(46,58,60,50)(49,59,64,56)(52,66,67,73)(54,70,69,63)(61,71,72,68);(38,39,40,41)(42,44)(43,48)(45,52)(46,54)(47,53)(49,61)(50,63)(51,62)(55,66)(56,68)(57,67)(58,70)(59,71)(60,69)(64,72)(65,73);(42,45,47,57)(43,49,51,64)(44,52,53,67)(46,59,60,56)(48,61,62,72)(50,65,58,55)(54,71,69,68)(63,73,70,66);(44,53)(48,62)(52,67)(54,69)(61,72)(63,70)(66,73)(68,71)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#24411, C₃₇×#25183, C₃₇×#25186, …
maximal normal subgroup of	C₃₇×#24411, C₃₇×#25183, C₃₇×#25186, …
maximal quotient of	C₃₇×#19402, C₃₇×#19403, C₃₇×#19404, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1776);

C37×#3044 #17991862