C₁₃×#9411 #15695750

order	3328
nilpotency class	3
isoclinism	isoclinic class of #9385
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#9411

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
prime radical	C₂⁵×C₁₃	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

606 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 606 conjugacy classes of subgroups — too many to draw. Only its 122 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)(14,15,18,24,34,41,17,31)(16,26,30,39,44,45,28,40)(19,25,33,42,20,22,35,23)(21,29,38,36,37,27,43,32);(14,16)(15,21,25,39)(17,32)(18,36)(19,27)(20,29)(22,40,41,37)(23,38,31,45)(24,26,42,43)(28,33)(30,35)(34,44);(15,22)(16,27)(17,33)(18,35)(21,37)(25,41)(26,43)(28,30)(29,44)(32,36)(38,45)(39,40)

Conjugacy classes & character table

481 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 2399);