Finite Group Databasebeta

C7×D4×C3⋊C8 #13056045

order1344
automorphism?
homologyAbelianization (H1) = C22×C7×C8 · Schur multiplier (H2) = C23

Aliases

direct productC7×D4×C3⋊C8

Splittings

HallC3×C7 ⋊ C8×D4
SylowC3 ⋊ C7×C8×D4

Subgroups

subgroupG/H
centerC2×C4×C7C22×D3
commutatorC2×C3C22×C7×C8
FrattiniC2×C4C22×D3×C7
FittingC3×C4×C7×D4C2
socleC22×C3×C7C22×C4
prime radicalC2×C3×C7×D4C4
cosocleC2×C3×C4C23×C7
hypercenterC4×C7×D4D3
hypocenterC3C7×C8×D4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C7 ◁ C4×C7×D4

268 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 672

Conjugacy classes & character table

420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 5334);