Finite Group Databasebeta

C2×C3⋊D3×#364 #72255498

order2304
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C3

Aliases

direct productC2×C3⋊D3×#364

Splittings

FittingC2×C32×#364 ⋊ C2
SylowC32 ⋊ C22×#364

Subgroups

subgroupG/H
centerC2×C8D4×C3⋊D3
commutatorC32×C4C23×C8
FrattiniC2×C8C23×C3⋊D3
FittingC2×C32×#364C2
socleC22×C32C2×C4⋊C8
prime radicalC23×C3⋊D3M16
cosocleC2×C32×C8C24
hypercenterC2×#364C3⋊D3
hypocenterC32C22×#364
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#364

2346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C3⋊D3×#1369
maximal normal subgroup ofC2×C3⋊D3×#1369

GAP

Past the SmallGroups library coverage — no SmallGroups id.