Finite Group Databasebeta

← Prev (#11675761) Next (#11675763) →

Dic6×AGL(1,ℤ/8) #11675762

order768
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productDic6×AGL(1,ℤ/8)

Splittings

SylowC3 ⋊ Q8×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×C4×AGL(1,ℤ/8)C2
socleC22×C3C23×D4
prime radicalC2×C3×AGL(1,ℤ/8)C22
hypercenterC4×AGL(1,ℤ/8)D3
hypocenterC3Q8×AGL(1,ℤ/8)
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

2010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

99 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1050143);