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C11×C5⋊(D7⋊C9) #20294145

order6930
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C5⋊(D7⋊C9)
unambiguous semidirect productC5⋊(C11×D7⋊C9)
unambiguous semidirect product(C7⋊C9)⋊(D5×C11)
unambiguous semidirect productD35⋊(C9×C11)
unambiguous semidirect product(C11×D35)⋊C9

Splittings

derived, HallC5×C7 ⋊ C2×C9×C11
HallC5×C11×C7⋊C9 ⋊ C2
HallC11×D35 ⋊ C9
HallC11×C7⋊C9 ⋊ D5
HallC5×C7×C11 ⋊ C2×C9
HallC5×C7⋊C9 ⋊ C2×C11
HallC7×C11 ⋊ C9×D5
HallD35 ⋊ C9×C11
HallC7⋊C9 ⋊ D5×C11
HallC5×C11 ⋊ D7⋊C9
SylowC7 ⋊ C9×D5×C11
SylowC5 ⋊ C11×D7⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C11C5⋊AGL(1,𝔽7)
commutator, hypocenterC5×C7C2×C9×C11
FrattiniC3C11×C5⋊AGL(1,𝔽7)
Fitting, socleC3×C5×C7×C11C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C3×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

561 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×C5⋊(D7⋊C9), D5×C11×D7⋊C9, D55⋊(D7⋊C9), …
maximal normal subgroup ofD11×C5⋊(D7⋊C9), D5×C11×D7⋊C9, D55⋊(D7⋊C9), …
maximal quotient ofC11×(C7⋊C9)⋊Dic5, C2×C11×C5⋊(D7⋊C9), C11×C25⋊(D7⋊C9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 32);