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C23×C22⋊(C13⋊C9) #24924497

order10764
isoclinismisoclinic class of C22⋊(C13⋊C3)
automorphism?
homologyAbelianization (H1) = C9×C23 · Schur multiplier (H2) = C2

Aliases

direct productC23×C22⋊(C13⋊C9)
unambiguous semidirect productC22⋊(C23×C13⋊C9)
unambiguous semidirect productC13⋊(C23×C22⋊C9)
unambiguous semidirect product(C22×C23)⋊(C13⋊C9)
unambiguous semidirect product(C13×C23)⋊(C22⋊C9)

Splittings

derived, HallC22×C13 ⋊ C9×C23
HallC22×C13×C23 ⋊ C9
HallC13×C23 ⋊ C22⋊C9
HallC22×C23 ⋊ C13⋊C9
SylowC13 ⋊ C23×C22⋊C9
SylowC22 ⋊ C23×C13⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C23C22⋊(C13⋊C3)
commutator, hypocenterC22×C13C9×C23
FrattiniC3C23×C22⋊(C13⋊C3)
Fitting, socle, prime radicalC22×C3×C13×C23C3
cosocleC22×C3×C13C3×C23
LCSG ▷ C22×C13
UCSC1 ◁ C3×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 33);