Finite Group Databasebeta

← Prev (#20294147) Next (#20294149) →

C11⋊C5×D7⋊C9 #20294148

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

Aliases

direct productC11⋊C5×D7⋊C9
unambiguous semidirect productD7⋊(C9×C11⋊C5)
unambiguous semidirect product(C7⋊C9)⋊(C2×C11⋊C5)
unambiguous semidirect product(D7×C11⋊C5)⋊C9
unambiguous semidirect product(C11×D7⋊C9)⋊C5

Splittings

derived, HallC7×C11 ⋊ C2×C5×C9
HallC11⋊C5×C7⋊C9 ⋊ C2
HallC11×D7⋊C9 ⋊ C5
HallD7×C11⋊C5 ⋊ C9
HallC11×C7⋊C9 ⋊ C2×C5
HallC7×C11⋊C5 ⋊ C2×C9
HallC11×D7 ⋊ C5×C9
HallC7⋊C9 ⋊ C2×C11⋊C5
HallD7 ⋊ C9×C11⋊C5
SylowC11 ⋊ C5×D7⋊C9
SylowC7 ⋊ C2×C9×C11⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC3AGL(1,𝔽7)×C11⋊C5
commutator, hypocenterC7×C11C2×C5×C9
Fitting, socleC3×C7×C11C2×C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

147 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×D7⋊C9, C2×C11⋊C5×D7⋊C9, C5×C11⋊C5×D7⋊C9, …
maximal normal subgroup ofAGL(1,𝔽11)×D7⋊C9, C2×C11⋊C5×D7⋊C9, C5×C11⋊C5×D7⋊C9
maximal quotient ofC11⋊C5×Dic7⋊C9, C2×C11⋊C5×D7⋊C9, D7⋊C9×C11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 35);