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C3×Q8×AGL(1,𝔽8) #13062084

order1344
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×Q8×AGL(1,𝔽8)
unambiguous semidirect product(C23×C3×Q8)⋊C7

Splittings

Fitting, HallC23×C3×Q8 ⋊ C7
SylowC23×Q8 ⋊ C3×C7

Subgroups

subgroupG/H
centerC2×C3C22×AGL(1,𝔽8)
commutator, cosocleC24C22×C3×C7
FrattiniC2C22×C3×AGL(1,𝔽8)
FittingC23×C3×Q8C7
socleC24×C3C22×C7
prime radicalC2×C3×AGL(1,𝔽8)C22
hypercenterC3×Q8AGL(1,𝔽8)
hypocenterC23C3×C7×Q8
LCSG ▷ C24 ▷ C23
UCSC1 ◁ C2×C3 ◁ C3×Q8

166 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 11373);