C₆₁×#11836 #29515269

order	15616
nilpotency class	4
isoclinism	isoclinic class of #11836
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₆₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₆₁×#11836

Subgroups

	subgroup	G/H
center, socle	C₂×C₆₁	#1514
commutator	C₂×C₈	C₂²×C₄×C₆₁
Frattini, cosocle	C₂×M₁₆	C₂³×C₆₁
prime radical	C₆₁×#469	C₂²
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₆₁ ◁ C₂×C₄×C₆₁ ◁ C₄×M₁₆×C₆₁ ◁ G

286 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 90 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)(3,13,15,30)(4,18,20,25)(5,11)(6,9)(7,12)(8,14)(10,21,27,22)(16,26,17,29)(19,28)(23,32)(24,31)(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)(5,17)(6,16)(7,15)(9,23)(10,26)(11,28)(12,24)(13,18)(14,22)(20,32)(21,31)(25,30)(27,29);(2,9,12,11)(4,20)(8,23,24,28)(10,18,27,25)(13,29,30,26)(14,31)(19,32)(21,22)

Conjugacy classes & character table

1708 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 4824);