C₁₃×#13433 #15699772

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13432
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13433

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2044
commutator, Frattini, cosocle	C₂×#41	C₂³×C₁₃
prime radical	C₁₃×#535	C₂²
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#41 ◁ G

424 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 86 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)(15,20)(16,24)(17,28)(18,31)(21,35)(22,37)(23,29)(25,41)(26,43)(27,40)(32,34)(33,36)(38,42)(39,44);(14,15,19,23)(16,25,27,21)(17,29,28,20)(18,32,31,22)(24,38,40,36)(26,33,44,42)(30,34,45,37)(35,43,41,39);(14,16,17,26,19,27,28,44)(15,21,20,33,23,25,29,42)(18,24,30,39,31,40,45,43)(22,36,34,35,32,38,37,41)

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, 6421);