Finite Group Databasebeta

← Prev (#20294141) Next (#20294143) →

C5×C11⋊(D7⋊C9) #20294142

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

Aliases

direct productC5×C11⋊(D7⋊C9)
unambiguous semidirect product(C7⋊C9)⋊(C5×D11)
unambiguous semidirect product(C5×D77)⋊C9

Splittings

derived, HallC7×C11 ⋊ C2×C5×C9
HallC5×C11×C7⋊C9 ⋊ C2
HallC5×D77 ⋊ C9
HallC11×C7⋊C9 ⋊ C2×C5
HallC5×C7×C11 ⋊ C2×C9
HallC5×C7⋊C9 ⋊ D11
HallD77 ⋊ C5×C9
HallC7⋊C9 ⋊ C5×D11
HallC5×C11 ⋊ D7⋊C9
HallC5×C7 ⋊ C9×D11
SylowC11 ⋊ C5×D7⋊C9
SylowC7 ⋊ C5×C9×D11

Subgroups

subgroupG/H
center, hypercenterC3×C5C11⋊AGL(1,𝔽7)
commutator, hypocenterC7×C11C2×C5×C9
FrattiniC3C5×C11⋊AGL(1,𝔽7)
Fitting, socleC3×C5×C7×C11C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

480 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D11×D7⋊C9, D5×C11⋊(D7⋊C9), D55⋊(D7⋊C9), …
maximal normal subgroup ofC5×D11×D7⋊C9, D5×C11⋊(D7⋊C9), D55⋊(D7⋊C9), …
maximal quotient ofC5×C11⋊(Dic7⋊C9), C2×C5×C11⋊(D7⋊C9), C25×C11⋊(D7⋊C9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 29);