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AGL(1,𝔽7)×D71⋊C5 #44447167

order29820
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productAGL(1,𝔽7)×D71⋊C5
unambiguous semidirect productD7⋊(C3×D71⋊C5)
unambiguous semidirect productD71⋊(C5×AGL(1,𝔽7))
unambiguous semidirect product(AGL(1,𝔽7)×D71)⋊C5
unambiguous semidirect product(D7×D71⋊C5)⋊C3
unambiguous semidirect product(ΓL(1,𝔽8)×D71⋊C5)⋊C2
unambiguous semidirect product(AGL(1,𝔽7)×C71⋊C5)⋊C2
unambiguous semidirect product(ΓL(1,𝔽8)⋊(D71⋊C5))⋊C2

Splittings

Fitting, socle, derived, HallC7×C71 ⋊ C22×C3×C5
HallD7×D71⋊C5 ⋊ C3
HallΓL(1,𝔽8)×C71⋊C5 ⋊ C22
HallAGL(1,𝔽7)×D71 ⋊ C5
HallC7×C71⋊C5 ⋊ C22×C3
HallD7×D71 ⋊ C3×C5
HallΓL(1,𝔽8)×C71 ⋊ C22×C5
HallC71⋊C5 ⋊ C2×AGL(1,𝔽7)
SylowC71 ⋊ C2×C5×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C2×D71⋊C5
SylowC7 ⋊ C2×C3×D71⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C71C22×C3×C5
LCSG ▷ C7×C71
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 497

Conjugacy classes & character table

119 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 55);