Finite Group Databasebeta

← Prev (#11860268) Next (#11860270) →

AGL(1,ℤ/8)×Dic9 #11860269

order1152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×Dic9

Splittings

SylowC9 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C2×D4×D9
commutatorC4×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC2×C9×AGL(1,ℤ/8)C2
socleC22×C3C2×D3×D4
prime radicalC2×C3×AGL(1,ℤ/8)D3
cosocleC2×C4×C9C24
hypercenterC2×AGL(1,ℤ/8)D9
hypocenterC9C4×AGL(1,ℤ/8)
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

822 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 94280);