Finite Group Databasebeta

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D9×D385 #28357448

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

Aliases

direct productD9×D385
unambiguous semidirect product(C5×D9)⋊D77
unambiguous semidirect product(C7×D9)⋊D55
unambiguous semidirect product(C11×D9)⋊D35

Splittings

Fitting, derived, HallC5×C7×C9×C11 ⋊ C22
HallC7×C9×C11 ⋊ C2×D5
HallC5×C9×C11 ⋊ C2×D7
HallC5×C7×C11 ⋊ C2×D9
HallC5×C7×C9 ⋊ C2×D11
HallC9×C11 ⋊ C2×D35
HallC7×C11 ⋊ D5×D9
HallC7×C9 ⋊ C2×D55
HallC5×C11 ⋊ D7×D9
HallC5×C9 ⋊ C2×D77
HallC5×C7 ⋊ D9×D11
SylowC11 ⋊ D9×D35
SylowC9 ⋊ C2×D385
SylowC7 ⋊ D9×D55
SylowC5 ⋊ D9×D77

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC5×C7×C9×C11C22
FrattiniC3D3×D385
socleC3×C5×C7×C11C2×D3
LCSG ▷ C5×C7×C9×C11
UCSC1

120 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 37 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

1164 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 115);