C₁₃×#32857 #15719196

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

Aliases

direct product

C₁₃×#32857

Subgroups

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

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

normal subgroups only

This group has 510 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) = 53
transitive degree	μ_t(G) = 3328

A minimal faithful permutation representation — 4 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,16)(19,20)(22,23,26,29)(24,30,32,27)(25,28,34,37)(31,36,33,35)(38,39,41,43)(40,46,48,44)(42,45,49,51)(47,52,50,53);(14,15,18,16)(17,19,21,20)(22,24,26,32)(23,27,29,30)(25,33,34,31)(28,36,37,35)(39,43)(40,47)(42,49)(44,52)(46,53)(48,50);(14,16,18,15)(17,19,21,20)(25,34)(28,37)(31,33)(35,36)(38,40,41,48)(39,44,43,46)(42,50,49,47)(45,52,51,53);(14,17,18,21)(15,19,16,20)(22,25,26,34)(23,28,29,37)(24,31,32,33)(27,35,30,36)(39,43)(40,48)(45,51)(47,50)

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, 25845);