C₁₃×#13333 #15699672

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13331
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#13333

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#459
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂×C₁₃×#135	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

546 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 122 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) = 49
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 49 points:

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

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, 6321);