Finite Group Databasebeta

← Prev (#27165231) Next (#27165233) →

C2×C3×D3×C71⋊C5 #27165232

order12780
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D3×C71⋊C5
unambiguous semidirect productC3⋊(C22×C3×C71⋊C5)
unambiguous semidirect product(C2×C3)⋊(C2×C3×C71⋊C5)
unambiguous semidirect product(C2×D3×C71)⋊(C3×C5)
unambiguous semidirect product(C2×C3×D3×C71)⋊C5

Splittings

Fitting, socleC2×C32×C71 ⋊ C2×C5
derivedC3×C71 ⋊ C22×C3×C5
HallC32×C71⋊C5 ⋊ C22
HallC2×C3×D3×C71 ⋊ C5
HallC32×C71 ⋊ C22×C5
SylowC71 ⋊ C2×C3×C5×D3
SylowC32 ⋊ C22×C71⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3D3×C71⋊C5
commutator, cosocle, hypocenterC3×C71C22×C3×C5
FrattiniC1G
Fitting, socleC2×C32×C71C2×C5
LCSG ▷ C3×C71
UCSC1 ◁ C2×C3

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

342 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12780, 68);