Finite Group Databasebeta

C2×C3⋊D3×#367 #72255343

order2304
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3

Aliases

direct productC2×C3⋊D3×#367

Splittings

FittingC2×C32×#367 ⋊ C2
SylowC32 ⋊ C22×#367

Subgroups

subgroupG/H
centerC23D8×C3⋊D3
commutatorC32×C8C23×C4
FrattiniC2×C8C23×C3⋊D3
FittingC2×C32×#367C2
socleC23×C32C2×D8
prime radicalC23×C3⋊D3D8
cosocleC2×C32×C8C24
hypercenterC2×#367C3⋊D3
hypocenterC32C22×#367
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#367

2346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1152

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C3⋊D3×#2177
maximal normal subgroup ofC2×C3⋊D3×#2177

GAP

Past the SmallGroups library coverage — no SmallGroups id.