C₁₃×#32901 #15719240

order	3328
nilpotency class	3
isoclinism	isoclinic class of #32898
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₁₃×#32901

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#585	C₂
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

3706 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 3706 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) = 832

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)(18,19,23,22)(20,24,28,27)(21,25,30,29)(26,32,33,31);(18,20)(19,24)(21,26)(22,27)(23,28)(25,31)(29,32)(30,33);(18,21)(19,25)(20,26)(22,29)(23,30)(24,31)(27,32)(28,33);(15,17)(18,22,23,19)(20,27,28,24)(21,29,30,25)(26,32,33,31)

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, 25889);