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C7×C11×D45 #20294129

order6930
isoclinismisoclinic class of D45
automorphism?
homologyAbelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×D45
unambiguous semidirect productC5⋊(C7×C11×D9)
unambiguous semidirect productC9⋊(C7×D5×C11)

Splittings

Fitting, HallC5×C7×C9×C11 ⋊ C2
derived, HallC5×C9 ⋊ C2×C7×C11
HallC7×C9×C11 ⋊ D5
HallC5×C9×C11 ⋊ C2×C7
HallC5×C7×C11 ⋊ D9
HallC5×C7×C9 ⋊ C2×C11
HallC9×C11 ⋊ C7×D5
HallC7×C9 ⋊ D5×C11
HallC5×C11 ⋊ C7×D9
HallC5×C7 ⋊ C11×D9
SylowC9 ⋊ C7×D5×C11
SylowC5 ⋊ C7×C11×D9

Subgroups

subgroupG/H
center, hypercenterC7×C11D45
commutator, hypocenterC5×C9C2×C7×C11
FrattiniC3C7×C11×D15
FittingC5×C7×C9×C11C2
socleC3×C5×C7×C11D3
LCSG ▷ C5×C9
UCSC1 ◁ C7×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1848 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×D11×D45, C11×D7×D45, D45×D77, …
maximal normal subgroup ofC7×D11×D45, C11×D7×D45, D45×D77, …
maximal quotient ofC7×C11×Dic45, C2×C7×C11×D45, C7×C11×D225, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 16);