C₁₃×#13361 #15699700

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13360
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#13361

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2021
commutator, Frattini, cosocle	C₂×#41	C₂³×C₁₃
prime radical	C₁₃×#3021	C₂
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#41 ◁ G

686 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 686 conjugacy classes of subgroups — too many to draw. Only its 94 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)(14,15,19,24)(16,25,29,40)(17,30,34,22)(18,21,35,23)(20,31,38,27)(26,43,28,42)(32,41,33,39)(36,44,37,45);(14,16)(15,20)(17,31)(18,26)(19,29)(21,37)(22,40)(23,36)(24,38)(25,30)(27,34)(28,35)(32,45)(33,44)(39,42)(41,43);(15,21)(16,26)(18,35)(22,39)(23,24)(25,40)(27,45)(28,29)(30,41)(31,44)(32,33)(36,37)

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, 6349);