C₁₃×#32899 #15719238

order	3328
nilpotency class	3
isoclinism	isoclinic class of #32898
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₁₃×#32899

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

3866 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 3866 conjugacy classes of subgroups — too many to draw. Only its 366 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) = 33
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 4 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(23,29)(30,33);(18,19)(20,23)(21,24)(22,25)(26,30)(27,29)(28,31)(32,33);(18,20)(19,23)(21,26)(22,27)(24,30)(25,29)(28,32)(31,33);(15,17)(18,21,22,28)(19,24,25,31)(20,26,27,32)(23,30,29,33)

Conjugacy classes & character table

637 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 25887);