C₃₇×#3516 #17992334

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

Aliases

direct product

C₃₇×#3516

Subgroups

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

1012 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)(47,50)(48,54)(53,57)(55,60);(46,47,51,50)(48,52,54,56)(49,57,58,53)(55,61,60,59);(38,39)(40,43)(41,42)(44,45)(46,48)(47,52)(49,55)(50,56)(51,54)(53,59)(57,61)(58,60);(46,49,51,58)(47,53,50,57)(48,55,54,60)(52,59,56,61);(38,40,41,44)(39,43,42,45)(46,50,51,47)(48,56,54,52)(49,57,58,53)(55,61,60,59)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#61472, C₃₇×#61473, C₃₇×#61490, …
maximal normal subgroup of	C₃₇×#61472, C₃₇×#61473, C₃₇×#61490, …
maximal quotient of	C₃₇×#34192, C₃₇×#34230, C₃₇×#34241, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2248);

C37×#3516 #17992334