Finite Group Databasebeta

← Prev (#13142510) Next (#13142512) →

C22⋊C4×3−1+2⋊C4 #13142511

order1728
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC22⋊C4×3−1+2⋊C4
unambiguous semidirect product(C22⋊C4×Dic9)⋊C3

Splittings

Sylow3−1+2 ⋊ C4×C22⋊C4

Subgroups

subgroupG/H
centerC23C22×AGL(1,ℤ/9)
commutatorC2×C9C2×C3×C42
Frattini, socleC23×C3C22×C3×D3
FittingC2×C22⋊C4×3−1+2C2
prime radicalC24×C32C2×D3
cosocleC23×C9C23×C3
hypercenterC2×C22⋊C4AGL(1,ℤ/9)
hypocenterC9C3×C4×C22⋊C4
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×C22⋊C4

840 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, 8574);