C₁₃×#32868 #15719207

order	3328
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#32868

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₁₃×#376 ◁ G

596 conjugacy classes of subgroups; only the 206 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 206 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) = 1664

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

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

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 25856);