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AGL(1,𝔽7)×#3757 #72247198

order6048
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24×C3

Aliases

direct productAGL(1,𝔽7)×#3757

Splittings

HallC32×ΓL(1,𝔽8) ⋊ C2×C22⋊C4
SylowC7 ⋊ C2×C3×#3757

Subgroups

subgroupG/H
center, FrattiniC22C2×C3⋊D3×AGL(1,𝔽7)
commutatorC2×C32×C7C22×C3×C4
FittingC23×C32×C7C22×C3
socle, cosocleC22×C32×C7C23×C3
prime radicalC23×C32×AGL(1,𝔽7)C2
hypercenterC23C3⋊D3×AGL(1,𝔽7)
hypocenterC32×C7C2×C3×C22⋊C4
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C22 ◁ C23

2656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 504

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC22⋊C4×C3⋊D3×AGL(1,𝔽7), AGL(1,𝔽7)×#64146
maximal normal subgroup ofC22⋊C4×C3⋊D3×AGL(1,𝔽7), AGL(1,𝔽7)×#64146

GAP

Past the SmallGroups library coverage — no SmallGroups id.