Finite Group Databasebeta

C22×D3×#568 #72272148

order1536
automorphism?
homologyAbelianization (H1) = C26×C4 · Schur multiplier (H2) = C220

Aliases

direct productC22×D3×#568

Splittings

FittingC22×C3×#568 ⋊ C2
SylowC3 ⋊ C23×#568

Subgroups

subgroupG/H
centerC22×C4C24×D3
commutatorC2×C3C26×C4
FrattiniC4C26×D3
FittingC22×C3×#568C2
socleC23×C3C24×C4
prime radicalC23×D3×#41C2
cosocleC3×C4C27
hypercenterC22×#568D3
hypocenterC3C23×#568
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C22×#568

115540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.