C₃₇×#3127 #17991945

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3008
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#3127

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₂³×C₃₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ #117×C₃₇ ◁ G

358 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 generators on 77 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)(46,47,50,54)(48,56,58,52)(49,60,61,69)(51,64,63,55)(53,65,68,62)(57,72,73,77)(59,67,75,71)(66,74,70,76);(39,42)(43,45)(46,48)(47,52)(49,57)(50,58)(51,59)(53,66)(54,56)(55,67)(60,77)(61,73)(62,74)(63,75)(64,71)(65,76)(68,70)(69,72);(46,49,50,61)(47,53,54,68)(48,57,58,73)(51,65,63,62)(52,66,56,70)(55,69,64,60)(59,76,75,74)(67,72,71,77);(38,40,41,44)(39,43,42,45)(48,58)(52,56)(57,73)(59,75)(66,70)(67,71)(72,77)(74,76)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₇×#3127, C₃₇×#60557, C₃₇×#60566, …
maximal normal subgroup of	C₂×C₃₇×#3127, C₃₇×#60557, C₃₇×#60566, …
maximal quotient of	C₃₇×#20745, C₃₇×#21127, C₃₇×#21135, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1859);

C37×#3127 #17991945