C₁₃×#32794 #15719133

order	3328
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₃×#32794

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

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

normal subgroups only

This group has 600 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) = 1664

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

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

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, 25782);