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C5×C11×D63 #20294127

order6930
isoclinismisoclinic class of D63
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×D63
unambiguous semidirect productC7⋊(C5×C11×D9)
unambiguous semidirect productC9⋊(C5×C11×D7)

Splittings

Fitting, HallC5×C7×C9×C11 ⋊ C2
derived, HallC7×C9 ⋊ C2×C5×C11
HallC7×C9×C11 ⋊ C2×C5
HallC5×C9×C11 ⋊ D7
HallC5×C7×C11 ⋊ D9
HallC5×C7×C9 ⋊ C2×C11
HallC9×C11 ⋊ C5×D7
HallC7×C11 ⋊ C5×D9
HallC5×C9 ⋊ C11×D7
HallC5×C7 ⋊ C11×D9
SylowC9 ⋊ C5×C11×D7
SylowC7 ⋊ C5×C11×D9

Subgroups

subgroupG/H
center, hypercenterC5×C11D63
commutator, hypocenterC7×C9C2×C5×C11
FrattiniC3C5×C11×D21
FittingC5×C7×C9×C11C2
socleC3×C5×C7×C11D3
LCSG ▷ C7×C9
UCSC1 ◁ C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1815 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D11×D63, C5×C11×D7×D9, C5×D63⋊D11, …
maximal normal subgroup ofC5×D11×D63, C5×C11×D7×D9, C5×D63⋊D11, …
maximal quotient ofC5×C11×Dic63, C2×C5×C11×D63, C11×C25×D63, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 14);