Finite Group Databasebeta

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D11×D585 #38787901

order25740
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD11×D585
unambiguous semidirect product(C5×D11)⋊D117
unambiguous semidirect product(C9×D11)⋊D65
unambiguous semidirect product(C13×D11)⋊D45

Splittings

Fitting, derived, HallC5×C9×C11×C13 ⋊ C22
HallC9×C11×C13 ⋊ C2×D5
HallC5×C11×C13 ⋊ C2×D9
HallC5×C9×C13 ⋊ C2×D11
HallC5×C9×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×D45
HallC9×C13 ⋊ D5×D11
HallC9×C11 ⋊ C2×D65
HallC5×C13 ⋊ D9×D11
HallC5×C11 ⋊ C2×D117
HallC5×C9 ⋊ D11×D13
SylowC13 ⋊ D11×D45
SylowC11 ⋊ C2×D585
SylowC9 ⋊ D11×D65
SylowC5 ⋊ D11×D117

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC5×C9×C11×C13C22
FrattiniC3D11×D195
socleC3×C5×C11×C13C2×D3
LCSG ▷ C5×C9×C11×C13
UCSC1

120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 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) = 6435

Conjugacy classes & character table

2058 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 132);