C₁₃×#15172 #15701511

order	3328
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

direct product

C₁₃×#15172

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

2826 conjugacy classes of subgroups; only the 478 normal subgroups are shown.

normal subgroups only

This group has 2826 conjugacy classes of subgroups — too many to draw. Only its 478 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) = 1664

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

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

Conjugacy classes & character table

832 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 8160);