Finite Group Databasebeta

← Prev (#29503291) Next (#29503293) →

C3×D11×D115 #29503292

order15180
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D11×D115
unambiguous semidirect product(C5×D11)⋊(C3×D23)
unambiguous semidirect product(D11×C23)⋊(C3×D5)

Splittings

Fitting, socle, HallC3×C5×C11×C23 ⋊ C22
derived, HallC5×C11×C23 ⋊ C22×C3
HallC3×C11×C23 ⋊ C2×D5
HallC3×C5×C23 ⋊ C2×D11
HallC11×C23 ⋊ C2×C3×D5
HallC3×C5×C11 ⋊ C2×D23
HallC5×C23 ⋊ C2×C3×D11
HallC3×C23 ⋊ D5×D11
HallC5×C11 ⋊ C2×C3×D23
HallC3×C11 ⋊ C2×D115
SylowC23 ⋊ C3×D5×D11
HallC3×C5 ⋊ D11×D23
SylowC11 ⋊ C2×C3×D115
SylowC5 ⋊ C3×D11×D23

Subgroups

subgroupG/H
center, hypercenterC3D11×D115
commutator, cosocle, hypocenterC5×C11×C23C22×C3
FrattiniC1G
Fitting, socleC3×C5×C11×C23C22
LCSG ▷ C5×C11×C23
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3795

Conjugacy classes & character table

1239 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 78);