Finite Group Databasebeta

C3×Q8×C7⋊C8 #13055456

order1344
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C22

Aliases

direct productC3×Q8×C7⋊C8

Splittings

HallC3×C7 ⋊ C8×Q8
SylowC7 ⋊ C3×C8×Q8

Subgroups

subgroupG/H
centerC2×C3×C4C22×D7
commutatorC2×C7C22×C3×C8
FrattiniC2×C4C22×C3×D7
FittingC3×C4×C7×Q8C2
socle, prime radicalC22×C3×C7C22×C4
cosocleC2×C4×C7C23×C3
hypercenterC3×C4×Q8D7
hypocenterC7C3×C8×Q8
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×Q8

204 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1344

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4745);