Finite Group Databasebeta

← Prev (#24926793) Next (#24926795) →

C2×C3×D3×C61⋊C5 #24926794

order10980
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D3×C61⋊C5
unambiguous semidirect productC3⋊(C22×C3×C61⋊C5)
unambiguous semidirect product(C2×C3)⋊(C2×C3×C61⋊C5)
unambiguous semidirect product(C2×C3×D3×C61)⋊C5

Splittings

Fitting, socleC2×C32×C61 ⋊ C2×C5
derivedC3×C61 ⋊ C22×C3×C5
HallC32×C61⋊C5 ⋊ C22
HallC2×C3×D3×C61 ⋊ C5
HallC32×C61 ⋊ C22×C5
SylowC61 ⋊ C2×C3×C5×D3
SylowC32 ⋊ C22×C61⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3D3×C61⋊C5
commutator, cosocle, hypocenterC3×C61C22×C3×C5
FrattiniC1G
Fitting, socleC2×C32×C61C2×C5
LCSG ▷ C3×C61
UCSC1 ◁ C2×C3

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

306 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10980, 144);