Finite Group Databasebeta

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C9×C23×#261 #24924484

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

Aliases

direct productC9×C23×#261

Splittings

Fitting, HallC9×C13×C23 ⋊ C4
derived, SylowC13 ⋊ C4×C9×C23
HallC13×C23 ⋊ C4×C9
HallC9×C13 ⋊ C4×C23

Subgroups

subgroupG/H
center, hypercenterC9×C23#261
commutator, hypocenterC13C4×C9×C23
FrattiniC3C3×C23×#261
FittingC9×C13×C23C4
socleC3×C13×C23C3×C4
prime radicalC3×C23×D13C2×C3
cosocleC3×D13C2×C3×C23
LCSG ▷ C13
UCSC1 ◁ C9×C23

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1449 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 20);