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C2×C23×D13⋊C9 #24924481

order10764
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C22×C9×C23 · Schur multiplier (H2) = C2

Aliases

direct productC2×C23×D13⋊C9
unambiguous semidirect productD13⋊(C2×C9×C23)
unambiguous semidirect product(C2×D13)⋊(C9×C23)
unambiguous semidirect product(C13⋊C9)⋊(C22×C23)
unambiguous semidirect product(C2×C13⋊C9)⋊(C2×C23)
unambiguous semidirect product(C2×C23×D13)⋊C9

Splittings

derived, SylowC13 ⋊ C22×C9×C23
HallC23×C13⋊C9 ⋊ C22
HallC2×C23×D13 ⋊ C9
HallC13×C23 ⋊ C22×C9
HallC13⋊C9 ⋊ C22×C23
HallC2×D13 ⋊ C9×C23

Subgroups

subgroupG/H
center, hypercenterC2×C3×C23D13⋊C3
commutator, hypocenterC13C22×C9×C23
FrattiniC3C2×C23×D13⋊C3
Fitting, socleC2×C3×C13×C23C2×C3
prime radicalC2×C3×C23×D13C3
cosocleC3×C13C22×C3×C23
LCSG ▷ C13
UCSC1 ◁ C2×C3×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, 17);