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D5×C11×C7⋊C9 #20294143

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

Aliases

direct productD5×C11×C7⋊C9
unambiguous semidirect productC5⋊(C2×C11×C7⋊C9)
unambiguous semidirect product(C7×D5)⋊(C9×C11)
unambiguous semidirect product(C7×D5×C11)⋊C9

Splittings

derived, HallC5×C7 ⋊ C2×C9×C11
HallC5×C11×C7⋊C9 ⋊ C2
HallC7×D5×C11 ⋊ C9
HallC5×C7×C11 ⋊ C2×C9
HallC5×C7⋊C9 ⋊ C2×C11
HallC7×C11 ⋊ C9×D5
HallC7×D5 ⋊ C9×C11
HallC5×C11 ⋊ C2×C7⋊C9
SylowC7 ⋊ C9×D5×C11
SylowC5 ⋊ C2×C11×C7⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C11D5×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C2×C9×C11
FrattiniC3D5×C11×ΓL(1,𝔽8)
Fitting, socleC3×C5×C7×C11C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C3×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

660 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×(C7⋊C9)⋊AGL(1,𝔽5), C11⋊((C7⋊C9)⋊AGL(1,𝔽5)), C11×AGL(1,𝔽5)×C7⋊C9, …
maximal normal subgroup ofC11×(C7⋊C9)⋊AGL(1,𝔽5), C11⋊((C7⋊C9)⋊AGL(1,𝔽5)), C11×AGL(1,𝔽5)×C7⋊C9, …
maximal quotient ofC11×Dic5×C7⋊C9, C2×D5×C11×C7⋊C9, C11×D25×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 30);