C₁₃×#32873 #15719212

order	3328
nilpotency class	3
isoclinism	isoclinic class of #32873
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₁₃×#32873

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2840
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂⁴×C₁₃ ◁ G

854 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 854 conjugacy classes of subgroups — too many to draw. Only its 186 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 — 4 generators on 29 points:

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

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 25861);