Finite Group Databasebeta

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D11×C23×D15 #29503307

order15180
automorphism?
homologyAbelianization (H1) = C22×C23 · Schur multiplier (H2) = C2

Aliases

direct productD11×C23×D15
unambiguous semidirect product(C3×D11)⋊(D5×C23)
unambiguous semidirect product(C5×D11)⋊(D3×C23)

Splittings

Fitting, socle, HallC3×C5×C11×C23 ⋊ C22
derived, HallC3×C5×C11 ⋊ C22×C23
HallC5×C11×C23 ⋊ C2×D3
HallC3×C11×C23 ⋊ C2×D5
HallC3×C5×C23 ⋊ C2×D11
HallC11×C23 ⋊ C2×D15
HallC5×C23 ⋊ D3×D11
HallC3×C23 ⋊ D5×D11
HallC5×C11 ⋊ C2×D3×C23
HallC3×C11 ⋊ C2×D5×C23
HallC3×C5 ⋊ C2×D11×C23
SylowC11 ⋊ C2×C23×D15
SylowC5 ⋊ D3×D11×C23
SylowC3 ⋊ D5×D11×C23

Subgroups

subgroupG/H
center, hypercenterC23D11×D15
commutator, cosocle, hypocenterC3×C5×C11C22×C23
FrattiniC1G
Fitting, socleC3×C5×C11×C23C22
LCSG ▷ C3×C5×C11
UCSC1 ◁ C23

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3795

Conjugacy classes & character table

1449 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 93);