Finite Group Databasebeta

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C3×D55⋊D23 #29503294

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

Aliases

direct productC3×D55⋊D23
unambiguous semidirect productD55⋊(C3×D23)
unambiguous semidirect productD115⋊(C3×D11)
unambiguous semidirect productD253⋊(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 ⋊ D5×D23
SylowC23 ⋊ C3×D5×D11
HallC3×C5 ⋊ D11×D23
SylowC11 ⋊ C3×D5×D23
SylowC5 ⋊ C3×D11×D23

Subgroups

subgroupG/H
center, hypercenterC3D55⋊D23
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

1041 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 80);