Finite Group Databasebeta

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C13×C17×C22⋊(C13⋊C3) #46828375

order34476
automorphism?
homologyAbelianization (H1) = C3×C13×C17 · Schur multiplier (H2) = C2

Aliases

direct productC13×C17×C22⋊(C13⋊C3)
unambiguous semidirect productC22⋊(C13×C17×C13⋊C3)
unambiguous semidirect productC13⋊(A4×C13×C17)
unambiguous semidirect product(C22×C17)⋊(C13×C13⋊C3)
unambiguous semidirect product(C13×C17)⋊(A4×C13)

Splittings

Fitting, socle, HallC22×C132×C17 ⋊ C3
derivedC22×C13 ⋊ C3×C13×C17
HallC132×C17 ⋊ A4
HallC22×C132 ⋊ C3×C17
SylowC132 ⋊ A4×C17
HallC22×C17 ⋊ C13×C13⋊C3
SylowC22 ⋊ C13×C17×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC13×C17C22⋊(C13⋊C3)
commutator, cosocle, hypocenterC22×C13C3×C13×C17
FrattiniC1G
Fitting, socleC22×C132×C17C3
LCSG ▷ C22×C13
UCSC1 ◁ C13×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1326

Conjugacy classes & character table

4420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34476, 256);