Finite Group Databasebeta

← Prev (#72271232) Next (#72271234) →

D3×#359428 #72271233

order3072
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C214

Aliases

direct productD3×#359428

Splittings

FittingC3×#359428 ⋊ C2
SylowC3 ⋊ C2×#359428

Subgroups

subgroupG/H
centerC23C22×D3×C22⋊C4
commutatorC24×C3C24×C4
FrattiniC25C24×D3
FittingC3×#359428C2
socleC23×C3C23×C22⋊C4
prime radicalC23×D3×#120C2
cosocleC25×C3C25
hypercenter#359428D3
hypocenterC3C2×#359428
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C27 ◁ #359428

At least 8384 conjugacy classes of subgroups; only the 3263 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×#72214549
maximal normal subgroup ofD3×#72214549

GAP

Past the SmallGroups library coverage — no SmallGroups id.