C₁₃×#13536 #15699875

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13398
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#13536

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#481
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂³×C₁₃	C₂×SD₁₆
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#97 ◁ G

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

normal subgroups only

This group has 318 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) = 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)(18,19,25,42,37,47,21,28,24,29,39,26,23,30,22,38)(20,31,40,44,41,46,32,45,35,43,36,27,34,49,33,48);(14,15)(16,17)(19,26,29,42)(21,25)(22,39)(23,37)(27,43,44,31)(28,30,38,47)(32,40)(33,36)(34,41)(45,49,48,46);(15,17)(18,20,24,35)(19,27,29,44)(21,36,22,40)(23,41,37,34)(25,33,39,32)(26,31,42,43)(28,46,38,49)(30,48,47,45)

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, 6524);