C₃₇×#3117 #17991935

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#3117

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	#121×C₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

386 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 2368

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#9531, C₃₇×#18159, C₃₇×#18161, …
maximal normal subgroup of	C₃₇×#9531, C₃₇×#18159, C₃₇×#18161, …
maximal quotient of	C₃₇×#20741, C₃₇×#21123, C₃₇×#21124, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1849);

C37×#3117 #17991935