Finite Group Databasebeta

C2×#11772675 #72255477

order2304
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C3

Aliases

direct productC2×#11772675

Splittings

SylowC32 ⋊ C2×#1398

Subgroups

subgroupG/H
centerC2×C8C4×C3⋊Dic3
commutatorC32×C4C2×C4×C8
FrattiniC2×C16C22×C3⋊D3
FittingC2×C32×#346C2
socleC22×C32#346
prime radicalC23×C32M32
cosocleC2×C32×C16C23
hypercenterC2×#346C3⋊D3
hypocenterC32C2×#1398
LCSG ▷ C32×C4 ▷ C32
UCSC1 ◁ C2×C8 ◁ C2×#346

666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C3⋊D3×#1398, C2×#72245373, C2×#72245413, …
maximal normal subgroup ofC2×C3⋊D3×#1398, C2×#72245373, C2×#72245413, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.