C₃₇×#3068 #17991886

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3068
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#3068

Subgroups

	subgroup	G/H
center, socle	C₂×C₃₇	C₂×#121
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ G

466 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 592

A minimal faithful permutation representation — 4 generators on 53 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)(39,43)(40,46)(41,49)(45,51)(47,48)(50,53);(38,39,41,43,42,45,49,51)(40,44,47,50,48,52,46,53);(38,40)(39,44)(41,47)(42,48)(43,50)(45,52)(46,49)(51,53);(39,45)(43,51)(44,52)(50,53)

Conjugacy classes & character table

1073 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#24420, C₃₇×#24422, C₃₇×#24472, …
maximal normal subgroup of	C₃₇×#24420, C₃₇×#24422, C₃₇×#24472, …
maximal quotient of	C₃₇×#19162, C₃₇×#19165, C₃₇×#19166, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1800);

C37×#3068 #17991886