Finite Group Databasebeta

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D5×C11×D63 #28357442

order13860
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productD5×C11×D63
unambiguous semidirect product(C7×D5)⋊(C11×D9)
unambiguous semidirect product(C9×D5)⋊(C11×D7)

Splittings

Fitting, HallC5×C7×C9×C11 ⋊ C22
derived, HallC5×C7×C9 ⋊ C22×C11
HallC7×C9×C11 ⋊ C2×D5
HallC5×C9×C11 ⋊ C2×D7
HallC5×C7×C11 ⋊ C2×D9
HallC9×C11 ⋊ D5×D7
HallC7×C11 ⋊ D5×D9
HallC7×C9 ⋊ C2×D5×C11
HallC5×C11 ⋊ C2×D63
HallC5×C9 ⋊ C2×C11×D7
HallC5×C7 ⋊ C2×C11×D9
SylowC9 ⋊ D5×C11×D7
SylowC7 ⋊ D5×C11×D9
SylowC5 ⋊ C2×C11×D63

Subgroups

subgroupG/H
center, hypercenterC11D5×D63
commutator, cosocle, hypocenterC5×C7×C9C22×C11
FrattiniC3D5×C11×D21
FittingC5×C7×C9×C11C22
socleC3×C5×C7×C11C2×D3
LCSG ▷ C5×C7×C9
UCSC1 ◁ C11

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3465

Conjugacy classes & character table

1452 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 109);