Finite Group Databasebeta

← Prev (#13087191) Next (#13087193) →

C5×D3×(C2×D3)⋊C4 #13087192

order1440
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×D3×(C2×D3)⋊C4

Splittings

FittingC2×C32×C4×C5 ⋊ C22
HallC32×C5 ⋊ C2×C22⋊C4
SylowC32 ⋊ C2×C5×C22⋊C4

Subgroups

subgroupG/H
centerC22×C5C2×D32
commutatorC2×C32C22×C4×C5
FrattiniC22C2×C5×D32
FittingC2×C32×C4×C5C22
socleC22×C32×C5C23
prime radicalC22×C5×D32C2
cosocleC22×C32C23×C5
hypercenterC2×C4×C5D32
hypocenterC32C2×C5×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C5 ◁ C2×C4×C5

562 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 3509);