Finite Group Databasebeta

← Prev (#35234576) Next (#35234578) →

C2×ΓL(1,𝔽8)×C101⋊C5 #35234577

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

Aliases

direct productC2×ΓL(1,𝔽8)×C101⋊C5
unambiguous semidirect product(C2×C7)⋊(C3×C101⋊C5)
unambiguous semidirect product(C2×C101)⋊(C5×ΓL(1,𝔽8))
unambiguous semidirect product(C2×ΓL(1,𝔽8)×C101)⋊C5
unambiguous semidirect product(C2×C7×C101⋊C5)⋊C3

Splittings

Fitting, socle, HallC2×C7×C101 ⋊ C3×C5
derived, HallC7×C101 ⋊ C2×C3×C5
HallC2×C7×C101⋊C5 ⋊ C3
HallC2×ΓL(1,𝔽8)×C101 ⋊ C5
HallC7×C101⋊C5 ⋊ C2×C3
HallΓL(1,𝔽8)×C101 ⋊ C2×C5
HallC2×C101 ⋊ C5×ΓL(1,𝔽8)
SylowC101 ⋊ C2×C5×ΓL(1,𝔽8)
HallC2×C7 ⋊ C3×C101⋊C5
SylowC7 ⋊ C2×C3×C101⋊C5

Subgroups

subgroupG/H
center, hypercenterC2ΓL(1,𝔽8)×C101⋊C5
commutator, cosocle, hypocenterC7×C101C2×C3×C5
FrattiniC1G
Fitting, socleC2×C7×C101C3×C5
LCSG ▷ C7×C101
UCSC1 ◁ C2

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1414

Conjugacy classes & character table

250 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21210, 4);