C₁₃×#13532 #15699871

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13340
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#13532

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#493
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#2093
prime radical	C₂×C₁₃×#135	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#97 ◁ G

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

normal subgroups only

This group has 312 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) = 45
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 3 generators on 45 points:

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

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, 6520);