C₃₇×#2645 #17991463

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#2645

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

352 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 4 generators on 61 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)(38,39,42,40)(41,43,45,44)(48,52)(50,53)(54,55,58,56)(57,60,61,59);(39,40)(43,44)(46,47,49,51)(48,53,52,50)(54,56,58,55)(57,60,61,59);(38,40,42,39)(41,43,45,44)(46,48)(47,50)(49,52)(51,53)(54,57)(55,59)(56,60)(58,61);(38,41,42,45)(39,43,40,44)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#29438, C₃₇×#29439, C₃₇×#29440, …
maximal normal subgroup of	C₃₇×#29438, C₃₇×#29439, C₃₇×#29440, …
maximal quotient of	C₃₇×#14261, C₃₇×#14266, C₃₇×#14333, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1377);

C37×#2645 #17991463