Finite Group Databasebeta

← Prev (#72219475) Next (#72219477) →

C2×C3×C4×C5×C3⋊D3 #72219476

order2160
isoclinismisoclinic class of C3⋊D3
automorphism?
homologyAbelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×C3×C4×C5×C3⋊D3

Splittings

FittingC2×C33×C4×C5 ⋊ C2
derivedC32 ⋊ C22×C3×C4×C5
HallC33×C5 ⋊ C22×C4
SylowC33 ⋊ C22×C4×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C4×C5C3⋊D3
commutator, hypocenterC32C22×C3×C4×C5
FrattiniC2C22×C3×C5×C3⋊D3
FittingC2×C33×C4×C5C2
socleC22×C33×C5C22
prime radicalC22×C3×C5×C3⋊D3C2
cosocleC2×C32C23×C3×C5
LCSG ▷ C32
UCSC1 ◁ C2×C3×C4×C5

776 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C3×C4×C5×#157
maximal normal subgroup ofC2×C3×C4×C5×#157

GAP

Past the SmallGroups library coverage — no SmallGroups id.