C₁₃×#32948 #15719287

order	3328
nilpotency class	3
isoclinism	isoclinic class of #32947
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₁₃×#32948

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2847
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

1334 conjugacy classes of subgroups; only the 290 normal subgroups are shown.

normal subgroups only

This group has 1334 conjugacy classes of subgroups — too many to draw. Only its 290 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) = 45
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 4 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,20)(18,21)(22,30)(23,31)(24,32)(25,38)(26,33)(28,34)(35,44)(36,41)(37,42)(40,45);(14,15,21,32,19,24,18,20)(16,22,33,41,27,36,26,30)(17,23,34,42,29,37,28,31)(25,35,43,44,38,45,39,40);(14,16)(15,22)(17,25)(18,26)(19,27)(20,30)(21,33)(23,35)(24,36)(28,39)(29,38)(31,40)(32,41)(34,43)(37,45)(42,44);(14,17)(15,23)(16,25)(18,28)(19,29)(20,31)(21,34)(22,35)(24,37)(26,39)(27,38)(30,40)(32,42)(33,43)(36,45)(41,44)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 25936);