C₆₁×#13340 #29516773

order	15616
nilpotency class	4
isoclinism	isoclinic class of #13340
automorphism	?
homology	Abelianization (H₁) = C₂³×C₆₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₆₁×#13340

Subgroups

	subgroup	G/H
center	C₄×C₆₁	#493
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₆₁
socle	C₂×C₆₁	#2011
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₆₁ ◁ C₂²×C₄×C₆₁ ◁ C₂×#97×C₆₁ ◁ G

552 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 118 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)(3,14)(4,11)(5,10)(6,24)(7,12)(8,15)(9,16)(13,20)(17,26)(18,32)(19,29)(21,31)(22,27)(23,30)(25,28)(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);(1,3)(2,8)(4,19)(5,15)(6,25)(7,18)(9,24)(10,28)(11,14)(12,27)(13,29)(16,21)(17,20)(22,23)(26,30)(31,32);(1,3)(2,9)(4,16)(5,22)(6,25)(7,18)(8,13)(10,14)(11,26)(12,29)(15,23)(17,20)(19,21)(24,27)(28,31)(30,32)

Conjugacy classes & character table

2074 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 6328);