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D9×C23×D13 #24924491

order10764
automorphism?
homologyAbelianization (H1) = C22×C23 · Schur multiplier (H2) = C2

Aliases

direct productD9×C23×D13
unambiguous semidirect product(C13×D9)⋊(C2×C23)
unambiguous semidirect product(C9×D13)⋊(C2×C23)
unambiguous semidirect productD117⋊(C2×C23)

Splittings

Fitting, HallC9×C13×C23 ⋊ C22
derived, HallC9×C13 ⋊ C22×C23
HallC13×C23 ⋊ C2×D9
HallC9×C23 ⋊ C2×D13
SylowC13 ⋊ C2×D9×C23
SylowC9 ⋊ C2×C23×D13

Subgroups

subgroupG/H
center, hypercenterC23D9×D13
commutator, cosocle, hypocenterC9×C13C22×C23
FrattiniC3D3×C23×D13
FittingC9×C13×C23C22
socleC3×C13×C23C2×D3
LCSG ▷ C9×C13
UCSC1 ◁ C23

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 27);