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C2×D3×D4×AGL(1,𝔽7) #72244129

order4032
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C210

Aliases

direct productC2×D3×D4×AGL(1,𝔽7)

Splittings

FittingC2×C3×C7×D4 ⋊ C22×C3
HallC3×ΓL(1,𝔽8) ⋊ C23×D4
SylowC7 ⋊ C22×C3×D3×D4

Subgroups

subgroupG/H
centerC22C22×D3×AGL(1,𝔽7)
commutator, cosocleC2×C3×C7C25×C3
FrattiniC2C23×D3×AGL(1,𝔽7)
FittingC2×C3×C7×D4C22×C3
socleC22×C3×C7C24×C3
hypercenterC2×D4D3×AGL(1,𝔽7)
hypocenterC3×C7C23×C3×D4
LCSG ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C2×D4

5684 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#120×AGL(1,𝔽7), D3×#127×AGL(1,𝔽7), D3×H(5,𝔽2)×AGL(1,𝔽7), …
maximal normal subgroup ofD3×#120×AGL(1,𝔽7), D3×#127×AGL(1,𝔽7), D3×H(5,𝔽2)×AGL(1,𝔽7), …
maximal quotient ofD3×#120×AGL(1,𝔽7), D3×#127×AGL(1,𝔽7), D3×AGL(1,ℤ/8)×AGL(1,𝔽7), …

GAP

Past the SmallGroups library coverage — no SmallGroups id.