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#13063889

order1404
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

Hall#66849 ⋊ C4
HallDic13 ⋊ 3−1+2
SylowC13 ⋊ C4×3−1+2

Subgroups

subgroupG/H
center, FrattiniC2×C3C3×D13⋊C3
commutatorC3×C13C32×C4
FittingC2×C9×C13C2×C3
socle, cosocleC2×C3×C13C2×C32
prime radicalC2×C3×C13⋊C3C2×C3
hypercenterC2×C9D13⋊C3
hypocenterC13C4×3−1+2
LCSG ▷ C3×C13 ▷ C13
UCSC1 ◁ C2×C3 ◁ C2×C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 468

Polycyclic presentation:

2,3^2,2,3,13|a^2=d,c^3=e^2,f^a=f^12,c^b=ce,f^b=f^3

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1404, 21);