C₃₇×#3521 #17992339

order	4736
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₃₇×#3521

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ G

1042 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 5 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)(39,42)(43,45)(46,47)(48,54)(49,57)(50,51)(52,56)(53,58)(55,59)(60,61);(47,51)(52,54)(53,57)(59,60);(38,39)(40,43)(41,42)(44,45)(46,48,50,56)(47,52,51,54)(49,55,58,61)(53,59,57,60);(46,47)(48,52)(49,53)(50,51)(54,56)(55,59)(57,58)(60,61);(38,40,41,44)(39,43,42,45)(46,49)(47,53)(48,55)(50,58)(51,57)(52,59)(54,60)(56,61)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#61486, C₃₇×#61487, C₃₇×#61500, …
maximal normal subgroup of	C₃₇×#61486, C₃₇×#61487, C₃₇×#61500, …
maximal quotient of	C₃₇×#34195, C₃₇×#34234, C₃₇×#34237, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2253);

C37×#3521 #17992339