C₁₃×#33567 #15719906

order	3328
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₃×#33567

Subgroups

	subgroup	G/H
center	C₄×C₁₃	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×Q₈	C₂⁴×C₁₃
socle	C₂×C₁₃	C₂×B(4,𝔽₂)
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#41 ◁ G

1184 conjugacy classes of subgroups; only the 218 normal subgroups are shown.

normal subgroups only

This group has 1184 conjugacy classes of subgroups — too many to draw. Only its 218 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)(16,24)(17,22)(18,21)(19,28)(20,25)(23,26)(27,29);(15,21)(16,19)(18,26)(22,24)(23,25)(28,29);(14,16)(17,26)(18,27)(19,20)(21,23)(24,28);(14,17,20,27)(15,22,25,29)(16,26,19,18)(21,24,23,28)

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 26555);