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C23×#261⋊C9 #24924478

order10764
isoclinismisoclinic class of AGL(1,𝔽13)
automorphism?
homologyAbelianization (H1) = C4×C9×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×#261⋊C9
unambiguous semidirect product#261⋊(C9×C23)
unambiguous semidirect product(C23×#261)⋊C9

Splittings

derived, SylowC13 ⋊ C4×C9×C23
HallC23×C13⋊C9 ⋊ C4
HallC23×#261 ⋊ C9
HallC13×C23 ⋊ C4×C9
HallC13⋊C9 ⋊ C4×C23
Hall#261 ⋊ C9×C23

Subgroups

subgroupG/H
center, hypercenterC3×C23AGL(1,𝔽13)
commutator, hypocenterC13C4×C9×C23
FrattiniC3C23×AGL(1,𝔽13)
Fitting, socleC3×C13×C23C3×C4
prime radicalC3×C23×D13C2×C3
cosocleC3×D13C2×C3×C23
LCSG ▷ C13
UCSC1 ◁ C3×C23

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

897 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 14);