Finite Group Databasebeta

← Prev (#20294133) Next (#20294135) →

C9×D7×C11⋊C5 #20294134

order6930
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×D7×C11⋊C5
unambiguous semidirect product(C9×C11×D7)⋊C5

Splittings

Fitting, HallC7×C9×C11 ⋊ C2×C5
derived, HallC7×C11 ⋊ C2×C5×C9
HallC7×C9×C11⋊C5 ⋊ C2
HallC9×C11×D7 ⋊ C5
HallC7×C11⋊C5 ⋊ C2×C9
HallC11×D7 ⋊ C5×C9
HallC9×C11 ⋊ C5×D7
HallC7×C9 ⋊ C2×C11⋊C5
SylowC11 ⋊ C5×C9×D7
SylowC7 ⋊ C2×C9×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC9D7×C11⋊C5
commutator, hypocenterC7×C11C2×C5×C9
FrattiniC3C3×D7×C11⋊C5
FittingC7×C9×C11C2×C5
socleC3×C7×C11C2×C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C9

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

315 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×D7×AGL(1,𝔽11), D7×C9⋊AGL(1,𝔽11), D7×D9×C11⋊C5, …
maximal normal subgroup ofC9×D7×AGL(1,𝔽11), D7×C9⋊AGL(1,𝔽11), D7×D9×C11⋊C5, …
maximal quotient ofC9×Dic7×C11⋊C5, C2×C9×D7×C11⋊C5, C9×D7×C11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 21);