C₆₁×#11917 #29515350

order	15616
nilpotency class	4
isoclinism	isoclinic class of #11915
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₆₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₆₁×#11917

Subgroups

	subgroup	G/H
center, socle	C₂×C₆₁	#1533
commutator	C₄²	C₂²×C₄×C₆₁
Frattini, cosocle	#97	C₂³×C₆₁
prime radical	C₆₁×#532	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₆₁ ◁ C₂×C₄×C₆₁ ◁ C₄×M₁₆×C₆₁ ◁ G

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

normal subgroups only

This group has 280 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:

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

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, 4905);