Finite Group Databasebeta

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C11×C23×D39 #34089407

order19734
automorphism?
homologyAbelianization (H1) = C2×C11×C23 · Schur multiplier (H2) = C1

Aliases

direct productC11×C23×D39
unambiguous semidirect productC3⋊(C11×C23×D13)
unambiguous semidirect productC13⋊(D3×C11×C23)

Splittings

Fitting, socle, HallC3×C11×C13×C23 ⋊ C2
derived, HallC3×C13 ⋊ C2×C11×C23
HallC11×C13×C23 ⋊ D3
HallC3×C13×C23 ⋊ C2×C11
HallC3×C11×C23 ⋊ D13
HallC3×C11×C13 ⋊ C2×C23
HallC13×C23 ⋊ D3×C11
HallC11×C13 ⋊ D3×C23
HallC3×C23 ⋊ C11×D13
HallC3×C11 ⋊ C23×D13
SylowC13 ⋊ D3×C11×C23
SylowC3 ⋊ C11×C23×D13

Subgroups

subgroupG/H
center, hypercenterC11×C23D39
commutator, cosocle, hypocenterC3×C13C2×C11×C23
FrattiniC1G
Fitting, socleC3×C11×C13×C23C2
LCSG ▷ C3×C13
UCSC1 ◁ C11×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9867

Conjugacy classes & character table

5313 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19734, 14);