Finite Group Databasebeta

← Prev (#24924487) Next (#24924489) →

C23×C9⋊#261 #24924488

order10764
isoclinismisoclinic class of C9⋊#261
automorphism?
homologyAbelianization (H1) = C4×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×C9⋊#261
unambiguous semidirect productC9⋊(C23×#261)

Splittings

Fitting, HallC9×C13×C23 ⋊ C4
derived, HallC9×C13 ⋊ C4×C23
HallC13×C23 ⋊ Dic9
HallC9×C23 ⋊ #261
SylowC13 ⋊ C23×Dic9
SylowC9 ⋊ C23×#261

Subgroups

subgroupG/H
center, hypercenterC23C9⋊#261
commutator, hypocenterC9×C13C4×C23
FrattiniC3C23×C3⋊#261
FittingC9×C13×C23C4
socleC3×C13×C23Dic3
prime radicalC3×C23×D13D3
cosocleC9×D13C2×C23
LCSG ▷ C9×C13
UCSC1 ◁ 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, 24);