Finite Group Databasebeta

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C17×D13×D33 #44415799

order29172
automorphism?
homologyAbelianization (H1) = C22×C17 · Schur multiplier (H2) = C2

Aliases

direct productC17×D13×D33
unambiguous semidirect product(C3×D13)⋊(C17×D11)
unambiguous semidirect product(C11×D13)⋊(D3×C17)

Splittings

Fitting, socle, HallC3×C11×C13×C17 ⋊ C22
derived, HallC3×C11×C13 ⋊ C22×C17
HallC11×C13×C17 ⋊ C2×D3
HallC3×C13×C17 ⋊ C2×D11
HallC3×C11×C17 ⋊ C2×D13
HallC13×C17 ⋊ C2×D33
HallC11×C17 ⋊ D3×D13
HallC11×C13 ⋊ C2×D3×C17
HallC3×C17 ⋊ D11×D13
HallC3×C13 ⋊ C2×C17×D11
HallC3×C11 ⋊ C2×C17×D13
SylowC13 ⋊ C2×C17×D33
SylowC11 ⋊ D3×C17×D13
SylowC3 ⋊ C17×D11×D13

Subgroups

subgroupG/H
center, hypercenterC17D13×D33
commutator, cosocle, hypocenterC3×C11×C13C22×C17
FrattiniC1G
Fitting, socleC3×C11×C13×C17C22
LCSG ▷ C3×C11×C13
UCSC1 ◁ C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7293

Conjugacy classes & character table

2448 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29172, 91);