Finite Group Databasebeta

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C13⋊C3×D255 #34091055

order19890
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC13⋊C3×D255
unambiguous semidirect productC3⋊(C13⋊C3×D85)
unambiguous semidirect productC5⋊(C13⋊C3×D51)
unambiguous semidirect productC17⋊(D15×C13⋊C3)
unambiguous semidirect product(C13×D255)⋊C3

Splittings

Fitting, socle, derivedC3×C5×C13×C17 ⋊ C2×C3
HallC3×C5×C17×C13⋊C3 ⋊ C2
HallC3×C17×C13⋊C3 ⋊ D5
HallC5×C13×C17 ⋊ C3×D3
HallC3×C5×C13⋊C3 ⋊ D17
HallC13×C17 ⋊ C3×D15
HallC3×C13⋊C3 ⋊ D85
HallC5×C17 ⋊ D3×C13⋊C3
HallC5×C13 ⋊ C3×D51
SylowC17 ⋊ D15×C13⋊C3
SylowC13 ⋊ C3×D255
SylowC5 ⋊ C13⋊C3×D51

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C13×C17C2×C3
LCSG ▷ C3×C5×C13×C17
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3315

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 40);