Finite Group Databasebeta

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D3×#72213693 #72247346

order58080
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C26

Aliases

direct productD3×#72213693

Splittings

FittingC22×C3×C112 ⋊ C23×C5
HallD3×#14515540 ⋊ C5
HallC3×#10597243 ⋊ C22×D4
Hall#10597243 ⋊ C2×D3×D4
HallC3×C112 ⋊ C22×C5×D4
SylowC112 ⋊ C2×C5×D3×D4
SylowC3 ⋊ C2×#72213693

Subgroups

subgroupG/H
center, FrattiniC2C2×D3×#11925892⋊C2
commutator, socle, cosocleC2×C3×C112C24×C5
FittingC22×C3×C112C23×C5
hypercenterC22D3×#11925892⋊C2
hypocenterC3×C112C22×C5×D4
LCSG ▷ C2×C3×C112 ▷ C3×C112
UCSC1 ◁ C2 ◁ C22

3228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 132

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

holomorph ofC3×Dic11, C2×C3×D11

GAP

Past the SmallGroups library coverage — no SmallGroups id.