C₁₃×#13076 #15699415

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13074
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#13076

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1893
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₁₃×#3060	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#131 ◁ G

466 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 146 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)(14,15,19,26,21,25,20,41)(16,27,30,33,29,45,31,37)(17,32,34,44,35,23,22,42)(18,36,38,43,40,28,39,24);(14,16,18,23,19,30,38,42,21,29,40,32,20,31,39,44)(15,22,43,45,41,35,36,33,25,34,24,27,26,17,28,37);(14,17)(15,23)(16,28)(18,37)(19,22)(20,34)(21,35)(24,31)(25,32)(26,44)(27,39)(29,36)(30,43)(33,40)(38,45)(41,42)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6064);