C₃₇×#2811 #17991629

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂×C₄²

Aliases

direct product

C₃₇×#2811

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

432 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)(41,44,45,43)(46,47)(48,52)(49,50)(51,53)(55,56)(59,60);(39,40)(41,45)(47,50)(48,53)(54,55,58,56)(57,60,61,59);(38,40,42,39)(41,44,45,43)(46,48)(47,51)(49,53)(50,52)(54,56,58,55)(57,60,61,59);(38,41,42,45)(39,43,40,44)(46,47)(48,51)(49,50)(52,53)(54,57)(55,59)(56,60)(58,61)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7749, C₃₇×#7759, C₃₇×#7812, …
maximal normal subgroup of	C₃₇×#7749, C₃₇×#7759, C₃₇×#7812, …
maximal quotient of	C₃₇×#14467, C₃₇×#14601, C₃₇×#15510, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1543);

C37×#2811 #17991629