C₁₃×#13683 #15700022

order	3328
nilpotency class	5
isoclinism	isoclinic class of #13681
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13683

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2196
commutator, Frattini, cosocle	C₄⋊Q₈	C₂³×C₁₃
prime radical	C₁₃×#3291	C₂
LCS	G ▷ C₄⋊Q₈ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₁₃×C₄⋊Q₈ ◁ G

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

normal subgroups only

This group has 392 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)(14,15,20,19)(16,24,27,29)(17,28,23,18)(21,26,22,25);(14,16)(15,21)(17,26)(18,29)(19,22)(20,27)(23,25)(24,28);(14,16)(15,22)(17,24)(18,25)(19,21)(20,27)(23,29)(26,28)

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, 6671);