Finite Group Databasebeta

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D4×3−1+2⋊C8 #13142751

order1728
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23

Aliases

direct productD4×3−1+2⋊C8
unambiguous semidirect product(D4×C9⋊C8)⋊C3

Splittings

Sylow3−1+2 ⋊ C8×D4

Subgroups

subgroupG/H
centerC2×C4C22×AGL(1,ℤ/9)
commutatorC2×C9C22×C3×C8
FrattiniC2×C3×C4C22×C3×D3
FittingC4×D4×3−1+2C2
socleC22×C3C22×C3×Dic3
prime radicalC2×C32×D4Dic3
cosocleC2×C4×C9C23×C3
hypercenterC4×D4AGL(1,ℤ/9)
hypocenterC9C3×C8×D4
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C4×D4

449 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 8814);