C₁₃×#13680 #15700019

order	3328
nilpotency class	5
isoclinism	isoclinic class of #13677
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13680

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2196
commutator, Frattini, cosocle	#124	C₂³×C₁₃
prime radical	C₁₃×#3289	C₂
LCS	G ▷ #124 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#124 ◁ G

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

normal subgroups only

This group has 378 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)(14,15,21,26)(16,27,30,31)(17,28,22,34)(18,33,36,23)(19,24,38,43)(20,39,41,25)(29,45,44,35)(32,42,40,37);(14,16)(15,22)(17,26)(18,34)(19,37)(20,29)(21,30)(23,31)(24,35)(25,40)(27,33)(28,36)(32,39)(38,42)(41,44)(43,45);(14,17,21,22)(15,16,26,30)(18,35,36,45)(19,31,38,27)(20,40,41,32)(23,42,33,37)(24,28,43,34)(25,44,39,29)

Conjugacy classes & character table

286 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6668);