C₁₃×#13425 #15699764

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13343
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13425

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂²×D₄	C₂³×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₁₃ ◁ C₂²×D₄×C₁₃ ◁ G

508 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 33
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,16)(18,19,23,20)(21,28,30,33)(22,27,32,25)(24,31,26,29);(14,15)(16,17)(18,20,23,19)(21,26,30,24)(22,25,32,27)(28,29,33,31);(14,16,17,15)(18,21)(19,24)(20,26)(22,31)(23,30)(25,33)(27,28)(29,32)

Conjugacy classes & character table

403 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6413);