Finite Group Databasebeta

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C13×C23×Dic9 #24924473

order10764
isoclinismisoclinic class of D9
automorphism?
homologyAbelianization (H1) = C4×C13×C23 · Schur multiplier (H2) = C1

Aliases

direct productC13×C23×Dic9
unambiguous semidirect productC9⋊(C4×C13×C23)

Splittings

derived, SylowC9 ⋊ C4×C13×C23
HallC9×C13×C23 ⋊ C4
HallC9×C23 ⋊ C4×C13
HallC9×C13 ⋊ C4×C23

Subgroups

subgroupG/H
center, hypercenterC2×C13×C23D9
commutator, hypocenterC9C4×C13×C23
FrattiniC2×C3D3×C13×C23
FittingC2×C9×C13×C23C2
socle, prime radicalC2×C3×C13×C23D3
cosocleC2×C9C2×C13×C23
LCSG ▷ C9
UCSC1 ◁ C2×C13×C23

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3588 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 9);