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C11×D315 #20294131

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

Aliases

direct productC11×D315
unambiguous semidirect productC5⋊(C11×D63)
unambiguous semidirect productC7⋊(C11×D45)
unambiguous semidirect productC9⋊(C11×D35)

Splittings

Fitting, HallC5×C7×C9×C11 ⋊ C2
derived, HallC5×C7×C9 ⋊ C2×C11
HallC7×C9×C11 ⋊ D5
HallC5×C9×C11 ⋊ D7
HallC5×C7×C11 ⋊ D9
HallC9×C11 ⋊ D35
HallC7×C11 ⋊ D45
HallC7×C9 ⋊ D5×C11
HallC5×C11 ⋊ D63
HallC5×C9 ⋊ C11×D7
HallC5×C7 ⋊ C11×D9
SylowC9 ⋊ C11×D35
SylowC7 ⋊ C11×D45
SylowC5 ⋊ C11×D63

Subgroups

subgroupG/H
center, hypercenterC11D315
commutator, hypocenterC5×C7×C9C2×C11
FrattiniC3C11×D105
FittingC5×C7×C9×C11C2
socleC3×C5×C7×C11D3
LCSG ▷ C5×C7×C9
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1749 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD11×D315, C11×D7×D45, D77⋊D45, …
maximal normal subgroup ofD11×D315, C11×D7×D45, D77⋊D45, …
maximal quotient ofC11×Dic315, C2×C11×D315, C11×D1575, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 18);