Finite Group Databasebeta

← Prev (#35234607) Next (#35234609) →

AGL(1,𝔽7)×C101⋊C5 #35234608

order21210
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽7)×C101⋊C5
unambiguous semidirect productD7⋊(C3×C101⋊C5)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C101⋊C5)
unambiguous semidirect product(AGL(1,𝔽7)×C101)⋊C5
unambiguous semidirect product(D7×C101⋊C5)⋊C3

Splittings

Fitting, socle, derived, HallC7×C101 ⋊ C2×C3×C5
HallΓL(1,𝔽8)×C101⋊C5 ⋊ C2
HallD7×C101⋊C5 ⋊ C3
HallAGL(1,𝔽7)×C101 ⋊ C5
HallC7×C101⋊C5 ⋊ C2×C3
HallΓL(1,𝔽8)×C101 ⋊ C2×C5
HallD7×C101 ⋊ C3×C5
SylowC101 ⋊ C5×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C2×C101⋊C5
HallD7 ⋊ C3×C101⋊C5
SylowC7 ⋊ C2×C3×C101⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C101C2×C3×C5
LCSG ▷ C7×C101
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 707

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21210, 35);