C₁₃×#13675 #15700014

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

Aliases

direct product

C₁₃×#13675

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2196
commutator, Frattini, cosocle	#127	C₂³×C₁₃
prime radical	C₁₃×#3292	C₂
LCS	G ▷ #127 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#127 ◁ G

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

normal subgroups only

This group has 408 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)(14,15,19,23)(16,24,27,28)(17,18,22,29)(20,26,21,25);(14,16)(15,20)(17,25)(18,24)(19,27)(21,23)(22,26)(28,29);(14,16)(15,21)(17,28)(18,26)(19,27)(20,23)(22,24)(25,29)

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, 6663);