Finite Group Databasebeta

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C32×C4×C13⋊C3 #13064035

order1404
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C33×C4 · Schur multiplier (H2) = C33

Aliases

direct productC32×C4×C13⋊C3
unambiguous semidirect product(C4×C13)⋊C33
unambiguous semidirect product(C3×C4×C13)⋊C32

Splittings

FittingC32×C4×C13 ⋊ C3
derived, SylowC13 ⋊ C33×C4
HallC4×C13 ⋊ C33

Subgroups

subgroupG/H
center, hypercenterC32×C4C13⋊C3
commutator, hypocenterC13C33×C4
FrattiniC2C2×C32×C13⋊C3
FittingC32×C4×C13C3
socleC2×C32×C13C2×C3
prime radicalC2×C32×C13⋊C3C2
cosocleC2×C13C2×C33
LCSG ▷ C13
UCSC1 ◁ C32×C4

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 468

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1404, 167);