C₆₁×#11547 #29514980

order	15616
nilpotency class	4
isoclinism	isoclinic class of #11541
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₆₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₆₁×#11547

Subgroups

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#99
commutator	C₂⁴	C₂²×C₄×C₆₁
Frattini, cosocle	C₂×C₂²⋊C₄	C₂³×C₆₁
prime radical	C₂⁵×C₆₁	C₂×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂⁴×C₆₁ ◁ C₂²×C₂²⋊C₄×C₆₁ ◁ G

492 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 102 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:

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

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, 4535);