Finite Group Databasebeta

← Prev (#44447205) Next (#44447207) →

D71×C5⋊AGL(1,𝔽7) #44447206

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

Aliases

direct productD71×C5⋊AGL(1,𝔽7)
unambiguous semidirect product(C5×D71)⋊AGL(1,𝔽7)
unambiguous semidirect product(ΓL(1,𝔽8)×D71)⋊D5
unambiguous semidirect product(D35×D71)⋊C3

Splittings

Fitting, socle, derived, HallC5×C7×C71 ⋊ C22×C3
HallD35×D71 ⋊ C3
HallC5×ΓL(1,𝔽8)×C71 ⋊ C22
HallΓL(1,𝔽8)×C71 ⋊ C2×D5
HallC7×C71 ⋊ C2×C3×D5
HallC5×C71 ⋊ C2×AGL(1,𝔽7)
HallC5×ΓL(1,𝔽8) ⋊ C2×D71
SylowC71 ⋊ C2×C5⋊AGL(1,𝔽7)
HallC5×C7 ⋊ C2×C3×D71
HallΓL(1,𝔽8) ⋊ D5×D71
SylowC7 ⋊ C3×D5×D71
SylowC5 ⋊ AGL(1,𝔽7)×D71

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C71C22×C3
LCSG ▷ C5×C7×C71
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2485

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 94);