C₃₇×#3524 #17992342

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

Aliases

direct product

C₃₇×#3524

Subgroups

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

1030 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#61486, C₃₇×#61488, C₃₇×#61500, …
maximal normal subgroup of	C₃₇×#61486, C₃₇×#61488, C₃₇×#61500, …
maximal quotient of	C₃₇×#34197, C₃₇×#34237, C₃₇×#34244, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2256);

C37×#3524 #17992342