Finite Group Databasebeta

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C13×D759 #34089410

order19734
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×D759
unambiguous semidirect productC3⋊(C13×D253)
unambiguous semidirect productC11⋊(C13×D69)
unambiguous semidirect productC23⋊(C13×D33)

Splittings

Fitting, socle, HallC3×C11×C13×C23 ⋊ C2
derived, HallC3×C11×C23 ⋊ C2×C13
HallC11×C13×C23 ⋊ D3
HallC3×C13×C23 ⋊ D11
HallC3×C11×C13 ⋊ D23
HallC13×C23 ⋊ D33
HallC11×C23 ⋊ D3×C13
HallC11×C13 ⋊ D69
HallC3×C23 ⋊ C13×D11
HallC3×C13 ⋊ D253
HallC3×C11 ⋊ C13×D23
SylowC23 ⋊ C13×D33
SylowC11 ⋊ C13×D69
SylowC3 ⋊ C13×D253

Subgroups

subgroupG/H
center, hypercenterC13D759
commutator, cosocle, hypocenterC3×C11×C23C2×C13
FrattiniC1G
Fitting, socleC3×C11×C13×C23C2
LCSG ▷ C3×C11×C23
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9867

Conjugacy classes & character table

4953 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19734, 17);