Finite Group Databasebeta

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C13×C23⋊(D19⋊C3) #46801780

order34086
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C23⋊(D19⋊C3)
unambiguous semidirect productC23⋊(C13×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(C13×D23)
unambiguous semidirect productD437⋊(C3×C13)

Splittings

Fitting, socle, HallC13×C19×C23 ⋊ C2×C3
derived, HallC19×C23 ⋊ C2×C3×C13
HallC13×C23×C19⋊C3 ⋊ C2
HallC13×D437 ⋊ C3
HallC23×C19⋊C3 ⋊ C2×C13
HallD437 ⋊ C3×C13
HallC13×C19⋊C3 ⋊ D23
HallC13×C23 ⋊ D19⋊C3
HallC13×C19 ⋊ C3×D23
HallC19⋊C3 ⋊ C13×D23
SylowC23 ⋊ C13×D19⋊C3
SylowC19 ⋊ C3×C13×D23

Subgroups

subgroupG/H
center, hypercenterC13C23⋊(D19⋊C3)
commutator, cosocle, hypocenterC19×C23C2×C3×C13
FrattiniC1G
Fitting, socleC13×C19×C23C2×C3
LCSG ▷ C19×C23
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5681

Conjugacy classes & character table

1404 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34086, 29);