C₁₃×#10216 #15696555

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10212
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#10216

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₁₃×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

468 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 832

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)(16,18)(17,20)(19,21)(22,23,28,33)(24,34,37,48)(25,38,41,46)(26,32,27,31)(29,42,44,36)(30,39,47,40)(35,43,51,45)(49,52,53,50);(15,18)(16,21)(19,20)(22,24)(23,29)(25,35)(26,42)(27,36)(28,37)(30,45)(31,48)(32,34)(33,44)(38,49)(39,52)(40,50)(41,51)(43,47)(46,53);(14,15,17,20)(16,19,21,18)(22,25,28,41)(23,30,33,47)(24,35,37,51)(26,40,27,39)(29,43,44,45)(31,38,32,46)(34,49,48,53)(36,52,42,50)

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 3204);