Finite Group Databasebeta

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C4×C23×C13⋊C9 #24924469

order10764
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C4×C9×C23 · Schur multiplier (H2) = C1

Aliases

direct productC4×C23×C13⋊C9
unambiguous semidirect product(C4×C13)⋊(C9×C23)
unambiguous semidirect product(C4×C13×C23)⋊C9

Splittings

derived, SylowC13 ⋊ C4×C9×C23
HallC4×C13×C23 ⋊ C9
HallC13×C23 ⋊ C4×C9
HallC4×C13 ⋊ C9×C23

Subgroups

subgroupG/H
center, hypercenterC3×C4×C23C13⋊C3
commutator, hypocenterC13C4×C9×C23
FrattiniC2×C3C2×C23×C13⋊C3
FittingC3×C4×C13×C23C3
socle, prime radicalC2×C3×C13×C23C2×C3
cosocleC2×C3×C13C2×C3×C23
LCSG ▷ C13
UCSC1 ◁ C3×C4×C23

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1932 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 5);