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C5×D11×C7⋊C9 #20294140

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

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C5ΓL(1,𝔽8)×D11
commutator, hypocenterC7×C11C2×C5×C9
FrattiniC3C5×ΓL(1,𝔽8)×D11
Fitting, socleC3×C5×C7×C11C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

525 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D11×D7⋊C9, D11×C5⋊(D7⋊C9), D5×D11×C7⋊C9, …
maximal normal subgroup ofC5×D11×D7⋊C9, D11×C5⋊(D7⋊C9), D5×D11×C7⋊C9, …
maximal quotient ofC5×Dic11×C7⋊C9, C2×C5×D11×C7⋊C9, D11×C25×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 27);