C₁₃×#13610 #15699949

order	3328
nilpotency class	5
isoclinism	isoclinic class of #13609
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₃×#13610

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2127
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	#127	C₂³×C₁₃
prime radical	C₁₃×#535	C₂²
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#535 ◁ G

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

normal subgroups only

This group has 336 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)(14,15)(16,25,27,20)(17,21)(18,23,33,22)(19,24)(26,40,41,34)(28,35,32,36)(29,42,43,45)(30,38)(31,37,44,39);(14,16,19,28)(15,20,24,36)(17,29,30,26)(18,32,33,27)(21,34,38,45)(22,35,23,25)(31,41,44,43)(37,40,39,42);(14,17)(15,21)(16,26)(18,31)(19,30)(20,34)(22,39)(23,37)(24,38)(25,40)(27,41)(28,29)(32,43)(33,44)(35,42)(36,45)

Conjugacy classes & character table

325 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6598);