C₆₁×#12436 #29515869

order	15616
nilpotency class	4
isoclinism	isoclinic class of #12436
automorphism	?
homology	Abelianization (H₁) = C₂³×C₆₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₆₁×#12436

Subgroups

	subgroup	G/H
center, socle	C₂×C₆₁	#1667
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₆₁
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₆₁ ◁ C₂×C₄×C₆₁ ◁ C₄×C₈×C₆₁ ◁ G

234 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 74 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:

(2,7)(3,12)(4,8)(5,17)(10,28)(11,22)(13,14)(15,29)(16,30)(18,23)(19,24)(20,21)(25,26)(31,32)(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);(1,2,8,21,5,10,18,22,6,11,23,28,17,20,4,7)(3,9,12,24,14,25,29,32,16,27,30,31,15,26,13,19);(1,3)(2,9)(4,13)(5,14)(6,16)(7,19)(8,12)(10,25)(11,27)(15,17)(18,29)(20,26)(21,24)(22,32)(23,30)(28,31)

Conjugacy classes & character table

2257 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 5424);