Finite Group Databasebeta

← Prev (#35234596) Next (#35234598) →

C7×C3⋊(D101⋊C5) #35234597

order21210
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊(D101⋊C5)
unambiguous semidirect productC3⋊(C7×D101⋊C5)
unambiguous semidirect product(C101⋊C5)⋊(D3×C7)
unambiguous semidirect productD303⋊(C5×C7)
unambiguous semidirect product(C7×D303)⋊C5

Splittings

Fitting, socle, HallC3×C7×C101 ⋊ C2×C5
derived, HallC3×C101 ⋊ C2×C5×C7
HallC3×C7×C101⋊C5 ⋊ C2
HallC7×D303 ⋊ C5
HallC7×C101⋊C5 ⋊ D3
HallC3×C101⋊C5 ⋊ C2×C7
HallC7×C101 ⋊ C5×D3
HallD303 ⋊ C5×C7
HallC101⋊C5 ⋊ D3×C7
SylowC101 ⋊ C5×D3×C7
HallC3×C7 ⋊ D101⋊C5
SylowC3 ⋊ C7×D101⋊C5

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(D101⋊C5)
commutator, cosocle, hypocenterC3×C101C2×C5×C7
FrattiniC1G
Fitting, socleC3×C7×C101C2×C5
LCSG ▷ C3×C101
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2121

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21210, 24);