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C2×#67×AGL(1,𝔽7) #72244117

order2016
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productC2×#67×AGL(1,𝔽7)

Splittings

FittingC23×C3×C7 ⋊ C22×C3
HallC3×ΓL(1,𝔽8) ⋊ C22×D4
SylowC7 ⋊ C22×C3×#67

Subgroups

subgroupG/H
centerC22C2×D3×AGL(1,𝔽7)
commutator, cosocleC2×C3×C7C24×C3
FrattiniC2C22×D3×AGL(1,𝔽7)
FittingC23×C3×C7C22×C3
socleC22×C3×C7C23×C3
hypercenterC23D3×AGL(1,𝔽7)
hypocenterC3×C7C22×C3×D4
LCSG ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C23

1078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D3×D4×AGL(1,𝔽7), AGL(1,𝔽7)×#937, AGL(1,𝔽7)×#953, …
maximal normal subgroup ofC2×D3×D4×AGL(1,𝔽7), AGL(1,𝔽7)×#937, AGL(1,𝔽7)×#953, …
maximal quotient ofAGL(1,𝔽7)×#937, AGL(1,𝔽7)×#953, AGL(1,𝔽7)×#940, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.