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C7×D9×C11⋊C5 #20294136

order6930
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D9×C11⋊C5
unambiguous semidirect productC9⋊(C2×C7×C11⋊C5)
unambiguous semidirect product(C11×D9)⋊(C5×C7)
unambiguous semidirect product(C7×C11×D9)⋊C5

Splittings

Fitting, HallC7×C9×C11 ⋊ C2×C5
derived, HallC9×C11 ⋊ C2×C5×C7
HallC7×C9×C11⋊C5 ⋊ C2
HallC7×C11×D9 ⋊ C5
HallC9×C11⋊C5 ⋊ C2×C7
HallC11×D9 ⋊ C5×C7
HallC7×C11 ⋊ C5×D9
HallC7×C9 ⋊ C2×C11⋊C5
SylowC11 ⋊ C5×C7×D9
SylowC9 ⋊ C2×C7×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC7D9×C11⋊C5
commutator, hypocenterC9×C11C2×C5×C7
FrattiniC3D3×C7×C11⋊C5
FittingC7×C9×C11C2×C5
socleC3×C7×C11C5×D3
LCSG ▷ C9×C11
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

294 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×D9×AGL(1,𝔽11), D9×C7⋊AGL(1,𝔽11), D7×D9×C11⋊C5, …
maximal normal subgroup ofC7×D9×AGL(1,𝔽11), D9×C7⋊AGL(1,𝔽11), D7×D9×C11⋊C5, …
maximal quotient ofC7×Dic9×C11⋊C5, C2×C7×D9×C11⋊C5, C7×D9×C11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 23);