C₁₃×#13518 #15699857

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13313
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#13518

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#466
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂³×C₁₃	#135
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

250 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 110 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 — 3 generators on 53 points:

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

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6506);