C₁₃×#12885 #15699224

order	3328
nilpotency class	3
isoclinism	isoclinic class of #2031
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#12885

Subgroups

	subgroup	G/H
center	C₈×C₁₃	#124
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#1832
prime radical	C₂³×C₁₃	#131
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₃ ◁ C₂²×C₈×C₁₃ ◁ G

234 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 122 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) = 832

A minimal faithful permutation representation — 3 generators on 77 points:

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

Conjugacy classes & character table

676 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5873);