C₁₃×#32900 #15719239

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

Aliases

direct product

C₁₃×#32900

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×H(5,𝔽₂)	C₂
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂⁵×C₁₃ ◁ G

4032 conjugacy classes of subgroups; only the 370 normal subgroups are shown.

normal subgroups only

This group has 4032 conjugacy classes of subgroups — too many to draw. Only its 370 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)(18,19,22,25)(20,23,27,30)(21,24,28,31)(26,32,33,29);(18,20)(19,23)(21,26)(22,27)(24,29)(25,30)(28,33)(31,32);(18,21)(19,24)(20,26)(22,28)(23,29)(25,31)(27,33)(30,32);(15,17)

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, 25888);