Finite Group Databasebeta

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C13×D11×D51 #44415804

order29172
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2

Aliases

direct productC13×D11×D51
unambiguous semidirect product(C3×D11)⋊(C13×D17)
unambiguous semidirect product(C17×D11)⋊(D3×C13)

Splittings

Fitting, socle, HallC3×C11×C13×C17 ⋊ C22
derived, HallC3×C11×C17 ⋊ C22×C13
HallC11×C13×C17 ⋊ C2×D3
HallC3×C13×C17 ⋊ C2×D11
HallC3×C11×C13 ⋊ C2×D17
HallC13×C17 ⋊ D3×D11
HallC11×C17 ⋊ C2×D3×C13
HallC11×C13 ⋊ C2×D51
HallC3×C17 ⋊ C2×C13×D11
HallC3×C13 ⋊ D11×D17
HallC3×C11 ⋊ C2×C13×D17
SylowC17 ⋊ D3×C13×D11
SylowC11 ⋊ C2×C13×D51
SylowC3 ⋊ C13×D11×D17

Subgroups

subgroupG/H
center, hypercenterC13D11×D51
commutator, cosocle, hypocenterC3×C11×C17C22×C13
FrattiniC1G
Fitting, socleC3×C11×C13×C17C22
LCSG ▷ C3×C11×C17
UCSC1 ◁ C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7293

Conjugacy classes & character table

2457 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29172, 96);