Finite Group Databasebeta

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C2×AGL(1,𝔽7)×#453 #72244379

order5376
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C210

Aliases

direct productC2×AGL(1,𝔽7)×#453

Splittings

FittingC2×C7×#453 ⋊ C2×C3
HallC2×D7×#453 ⋊ C3
HallΓL(1,𝔽8) ⋊ C22×#453
SylowC7 ⋊ C22×C3×#453

Subgroups

subgroupG/H
centerC22#120×AGL(1,𝔽7)
commutator, cosocleC2×C4×C7C25×C3
FrattiniC2×C4C24×AGL(1,𝔽7)
FittingC2×C7×#453C2×C3
socleC22×C7C2×C3×#120
hypercenterC2×#453AGL(1,𝔽7)
hypocenterC7C22×C3×#453
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#453

11340 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 112

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽7)×#5935, D3×AGL(1,𝔽7)×#453
maximal quotient ofD3×AGL(1,𝔽7)×#453

GAP

Past the SmallGroups library coverage — no SmallGroups id.