Finite Group Databasebeta

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C11×D45⋊D13 #38787907

order25740
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×D45⋊D13
unambiguous semidirect productD45⋊(C11×D13)
unambiguous semidirect productD65⋊(C11×D9)
unambiguous semidirect productD117⋊(D5×C11)

Splittings

Fitting, HallC5×C9×C11×C13 ⋊ C22
derived, HallC5×C9×C13 ⋊ C22×C11
HallC9×C11×C13 ⋊ C2×D5
HallC5×C11×C13 ⋊ C2×D9
HallC5×C9×C11 ⋊ C2×D13
HallC11×C13 ⋊ D5×D9
HallC9×C13 ⋊ C2×D5×C11
HallC9×C11 ⋊ D5×D13
HallC5×C13 ⋊ C2×C11×D9
HallC5×C11 ⋊ D9×D13
HallC5×C9 ⋊ C2×C11×D13
SylowC13 ⋊ D5×C11×D9
SylowC9 ⋊ D5×C11×D13
SylowC5 ⋊ C11×D9×D13

Subgroups

subgroupG/H
center, hypercenterC11D45⋊D13
commutator, cosocle, hypocenterC5×C9×C13C22×C11
FrattiniC3C11×D15⋊D13
FittingC5×C9×C11×C13C22
socleC3×C5×C11×C13C2×D3
LCSG ▷ C5×C9×C13
UCSC1 ◁ C11

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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 138);