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C3×D7×AGL(1,ℤ/8) #13061114

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

Aliases

direct productC3×D7×AGL(1,ℤ/8)

Splittings

FittingC3×C7×AGL(1,ℤ/8) ⋊ C2
HallC3×C7 ⋊ C2×AGL(1,ℤ/8)
SylowC7 ⋊ C2×C3×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C3C2×D4×D7
commutator, cosocleC4×C7C24×C3
FrattiniC4C23×C3×D7
FittingC3×C7×AGL(1,ℤ/8)C2
socleC2×C3×C7C22×D4
hypercenterC3×AGL(1,ℤ/8)D7
hypocenterC7C2×C3×AGL(1,ℤ/8)
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×AGL(1,ℤ/8)

596 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D7×#453, D3×D7×AGL(1,ℤ/8), D7×#5198, …
maximal normal subgroup ofC3×D7×#453, D3×D7×AGL(1,ℤ/8), D7×#5198, …
maximal quotient of#72245056, AGL(1,ℤ/8)×ΓL(1,𝔽8)⋊D7, C3×D7×#932, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 10403);