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AGL(1,𝔽7)×5−1+2 #72219014

order5250
automorphism?
homologyAbelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽7)×5−1+2

Splittings

Fitting, HallC7×5−1+2 ⋊ C2×C3
HallΓL(1,𝔽8)×5−1+2 ⋊ C2
HallD7×5−1+2 ⋊ C3
HallΓL(1,𝔽8) ⋊ C2×5−1+2
HallD7 ⋊ C3×5−1+2
SylowC7 ⋊ C2×C3×5−1+2

Subgroups

subgroupG/H
center, FrattiniC5C52×AGL(1,𝔽7)
commutator, socle, cosocleC5×C7C2×C3×C52
FittingC7×5−1+2C2×C3
prime radicalC52×AGL(1,𝔽7)C5
hypercenter5−1+2AGL(1,𝔽7)
hypocenterC7C2×C3×5−1+2
LCSG ▷ C5×C7 ▷ C7
UCSC1 ◁ C5 ◁ 5−1+2

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

203 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×D25⋊C5
maximal normal subgroup ofAGL(1,𝔽7)×D25⋊C5

GAP

Past the SmallGroups library coverage — no SmallGroups id.