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C13×D9×D11 #19104151

order5148
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2

Aliases

direct productC13×D9×D11
unambiguous semidirect product(C11×D9)⋊(C2×C13)
unambiguous semidirect product(C9×D11)⋊(C2×C13)
unambiguous semidirect productD99⋊(C2×C13)

Splittings

Fitting, HallC9×C11×C13 ⋊ C22
derived, HallC9×C11 ⋊ C22×C13
HallC11×C13 ⋊ C2×D9
HallC9×C13 ⋊ C2×D11
SylowC11 ⋊ C2×C13×D9
SylowC9 ⋊ C2×C13×D11

Subgroups

subgroupG/H
center, hypercenterC13D9×D11
commutator, hypocenterC9×C11C22×C13
FrattiniC3D3×C13×D11
FittingC9×C11×C13C22
socleC3×C11×C13C2×D3
LCSG ▷ C9×C11
UCSC1 ◁ C13

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

546 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13×D9×AGL(1,𝔽11), C5×C13×D9×D11, C13×D11×D45, …
maximal normal subgroup ofC13×D9×AGL(1,𝔽11), C5×C13×D9×D11, C7×C13×D9×D11
maximal quotient ofC5×C13×D9×D11, C13×D11×D45, C13×D9×D55, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5148, 27);