C₆₁×#23895 #29527328

order	15616
nilpotency class	3
isoclinism	isoclinic class of #23895
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₆₁ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₆₁×#23895

Subgroups

	subgroup	G/H
center, socle	C₂×C₆₁	#2403
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₆₁
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₆₁ ◁ C₂⁴×C₆₁ ◁ G

2002 conjugacy classes of subgroups; only the 282 normal subgroups are shown.

normal subgroups only

This group has 2002 conjugacy classes of subgroups — too many to draw. Only its 282 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) = 77
transitive degree	μ_t(G) = 976

A minimal faithful permutation representation — 4 generators on 77 points:

(1,2)(3,6)(4,7)(5,8)(9,15)(10,12)(11,14)(13,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77);(6,12)(13,15);(1,3)(2,6)(4,9)(5,10)(7,13)(8,12)(11,16)(14,15);(1,4)(2,7)(3,9)(5,11)(6,13)(8,14)(10,16)(12,15)

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, 16883);