C₆₁×#13472 #29516905

order	15616
nilpotency class	4
isoclinism	isoclinic class of #13472
automorphism	?
homology	Abelianization (H₁) = C₂³×C₆₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₆₁×#13472

Subgroups

	subgroup	G/H
center, socle	C₂×C₆₁	#2067
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₆₁
prime radical	C₂²×D₈×C₆₁	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₆₁ ◁ C₂²×C₄×C₆₁ ◁ C₆₁×#405 ◁ G

316 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 106 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:

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

Conjugacy classes & character table

2074 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 6460);