C₁₃×#13676 #15700015

order	3328
nilpotency class	5
isoclinism	isoclinic class of #13673
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13676

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2196
commutator, Frattini, cosocle	#127	C₂³×C₁₃
prime radical	C₁₃×#3291	C₂
LCS	G ▷ #127 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#127 ◁ G

394 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 58 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)(14,15,19,23)(16,20,26,34)(17,21,29,37)(18,30,31,22)(24,38,41,44)(25,33,42,43)(27,35,28,36)(32,40,45,39);(14,16,19,26)(15,20,23,34)(17,24,29,41)(18,25,31,42)(21,32,37,45)(22,33,30,43)(27,39,28,40)(35,38,36,44);(14,17)(15,21)(16,24)(18,27)(19,29)(20,32)(22,35)(23,37)(25,39)(26,41)(28,31)(30,36)(33,38)(34,45)(40,42)(43,44)

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, 6664);