C₃₇×#3585 #17992403

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3585
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₃₇×#3585

Subgroups

	subgroup	G/H
center, socle	C₂×C₃₇	C₂³×D₄
commutator, Frattini, cosocle	C₄	C₂⁵×C₃₇
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₇ ◁ C₂×#41×C₃₇ ◁ G

1464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 5 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)(38,39)(40,44)(41,43)(42,45)(46,49)(47,51)(48,50)(52,53);(39,43)(41,49)(44,50)(45,46)(48,53)(51,52);(38,40)(39,44)(41,48)(42,47)(43,50)(45,51)(46,52)(49,53);(40,47)(44,51)(48,53)(50,52);(39,45)(43,46)(44,51)(50,52)

Conjugacy classes & character table

1517 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#23872, C₃₇×#23874, C₃₇×#23882, …
maximal normal subgroup of	C₃₇×#23872, C₃₇×#23874, C₃₇×#23882, …
maximal quotient of	C₃₇×#60087, C₃₇×#60089, C₃₇×#60109, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2317);

C37×#3585 #17992403