Finite Group Databasebeta

← Prev (#29503290) Next (#29503292) →

C3×D5×D11×C23 #29503291

order15180
automorphism?
homologyAbelianization (H1) = C22×C3×C23 · Schur multiplier (H2) = C2

Aliases

direct productC3×D5×D11×C23
unambiguous semidirect product(D5×C11)⋊(C2×C3×C23)
unambiguous semidirect product(C5×D11)⋊(C2×C3×C23)
unambiguous semidirect productD55⋊(C2×C3×C23)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C23D5×D11
commutator, cosocle, hypocenterC5×C11C22×C3×C23
FrattiniC1G
Fitting, socleC3×C5×C11×C23C22
LCSG ▷ C5×C11
UCSC1 ◁ C3×C23

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3795

Conjugacy classes & character table

1932 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 77);