C₆₁×#13498 #29516931

order	15616
nilpotency class	4
isoclinism	isoclinic class of #13309
automorphism	?
homology	Abelianization (H₁) = C₂³×C₆₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₆₁×#13498

Subgroups

	subgroup	G/H
center	C₄×C₆₁	#469
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₆₁
socle	C₂×C₆₁	#2076
prime radical	C₂⁴×C₆₁	Q₁₆
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₆₁ ◁ C₂²×C₄×C₆₁ ◁ C₂³×C₈×C₆₁ ◁ G

292 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 93
transitive degree	μ_t(G) = 1952

A minimal faithful permutation representation — 3 generators on 93 points:

(1,2,4,8,16,23,30,32,6,9,18,24,5,10,17,25)(3,11,13,26,19,31,29,20,12,27,28,21,14,22,15,7)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(7,20)(11,27)(21,26)(22,31);(1,3,5,19,6,12,16,14)(2,7,10,26,9,20,23,21)(4,15,17,13,18,29,30,28)(8,22,25,11,24,31,32,27)

Conjugacy classes & character table

2440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 6486);