C₁₃×#10586 #15696925

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10078
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#10586

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

350 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 114 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 — 3 generators on 53 points:

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

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, 3574);