Finite Group Databasebeta

← Prev (#13061140) Next (#13061142) →

C2×C3×#6495 #13061141

order1344
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25

Aliases

direct productC2×C3×#6495

Splittings

FittingC22×C3×C7×D4 ⋊ C2
HallC3×C7 ⋊ C2×AGL(1,ℤ/8)
SylowC7 ⋊ C2×C3×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22×C3C2×C22⋊D7
commutator, cosocleC4×C7C24×C3
FrattiniC4C23×C3×D7
FittingC22×C3×C7×D4C2
socleC22×C3×C7C2×D4
hypercenterC22×C3×D4D7
hypocenterC7C2×C3×AGL(1,ℤ/8)
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×D4

596 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 336

Conjugacy classes & character table

246 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 10430);