C₁₃×#13677 #15700016

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

Aliases

direct product

C₁₃×#13677

Subgroups

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

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

normal subgroups only

This group has 420 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) = 29
transitive degree	μ_t(G) = 208

A minimal faithful permutation representation — 3 generators on 29 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,20)(16,23)(18,28)(21,25)(22,24)(26,29);(14,15)(16,24)(17,26)(18,21)(19,22)(20,23)(25,27)(28,29);(14,15)(16,25)(17,20)(18,29)(19,22)(21,28)(23,26)(24,27)

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, 6665);