Finite Group Databasebeta

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D3×#14796 #72270873

order1536
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productD3×#14796

Splittings

FittingC3×#14796 ⋊ C2
SylowC3 ⋊ C2×#14796

Subgroups

subgroupG/H
center, FrattiniC24C24×D3
commutator, socle, cosocleC24×C3C25
FittingC3×#14796C2
prime radicalC2×D3×#392C2
hypercenter#14796D3
hypocenterC3C2×#14796
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #14796

19556 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#1262353, D3×#4929019, D3×#1259281
maximal normal subgroup ofD3×#1262353, D3×#4929019, D3×#1259281

GAP

Past the SmallGroups library coverage — no SmallGroups id.