Finite Group Databasebeta

← Prev (#34089410) Next (#34089412) →

C23×D429 #34089411

order19734
automorphism?
homologyAbelianization (H1) = C2×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×D429
unambiguous semidirect productC3⋊(C23×D143)
unambiguous semidirect productC11⋊(C23×D39)
unambiguous semidirect productC13⋊(C23×D33)

Splittings

Fitting, socle, HallC3×C11×C13×C23 ⋊ C2
derived, HallC3×C11×C13 ⋊ C2×C23
HallC11×C13×C23 ⋊ D3
HallC3×C13×C23 ⋊ D11
HallC3×C11×C23 ⋊ D13
HallC13×C23 ⋊ D33
HallC11×C23 ⋊ D39
HallC11×C13 ⋊ D3×C23
HallC3×C23 ⋊ D143
HallC3×C13 ⋊ D11×C23
HallC3×C11 ⋊ C23×D13
SylowC13 ⋊ C23×D33
SylowC11 ⋊ C23×D39
SylowC3 ⋊ C23×D143

Subgroups

subgroupG/H
center, hypercenterC23D429
commutator, cosocle, hypocenterC3×C11×C13C2×C23
FrattiniC1G
Fitting, socleC3×C11×C13×C23C2
LCSG ▷ C3×C11×C13
UCSC1 ◁ C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9867

Conjugacy classes & character table

4968 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19734, 18);