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C2×D13×3−1+2 #13064012

order1404
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2

Aliases

direct productC2×D13×3−1+2

Splittings

FittingC2×C13×3−1+2 ⋊ C2
HallC13×3−1+2 ⋊ C22
SylowC13 ⋊ C22×3−1+2

Subgroups

subgroupG/H
centerC2×C3C32×D13
commutator, cosocleC3×C13C22×C32
FrattiniC3C2×C32×D13
FittingC2×C13×3−1+2C2
socleC2×C3×C13C2×C32
prime radicalC2×C32×D13C3
hypercenterC2×3−1+2D13
hypocenterC13C22×3−1+2
LCSG ▷ C3×C13 ▷ C13
UCSC1 ◁ C2×C3 ◁ C2×3−1+2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 234

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×3−1+2×#261, C2×D13×AGL(1,ℤ/9), C2×3−1+2⋊#261, …
maximal normal subgroup ofC2×3−1+2×#261, C2×D13×AGL(1,ℤ/9), C2×3−1+2⋊#261, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1404, 144);