C₆₁×#8795 #29512228

order	15616
nilpotency class	3
isoclinism	isoclinic class of #8794
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₆₁ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₆₁×#8795

Subgroups

	subgroup	G/H
center, socle	C₂²×C₆₁	#382
commutator	C₄²	C₂²×C₄×C₆₁
Frattini, cosocle	C₂×C₄²	C₂³×C₆₁
prime radical	C₂³×C₆₁	#124
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

270 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 101
transitive degree	μ_t(G) = 3904

A minimal faithful permutation representation — 3 generators on 101 points:

(2,7)(3,8)(4,5)(9,10)(11,19,23,15)(12,24,27,38)(13,18)(14,17)(16,26,32,35)(20,28)(21,36)(22,33,34,30)(25,39)(29,37)(31,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(1,2,4,7,6,8,5,3)(9,11,20,34,14,23,13,22)(10,15,28,33,17,19,18,30)(12,25,35,37,27,21,26,40)(16,31,38,39,32,29,24,36);(1,3,4,2,6,7,5,8)(9,12)(10,16,17,32)(11,21)(13,26)(14,27)(15,29,19,31)(18,24,28,38)(20,35)(22,37)(23,25)(30,39,33,36)(34,40)

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, 1783);