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C13×D765 #34091030

order19890
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×D765
unambiguous semidirect productC5⋊(C13×D153)
unambiguous semidirect productC9⋊(C13×D85)
unambiguous semidirect productC17⋊(C13×D45)

Splittings

Fitting, HallC5×C9×C13×C17 ⋊ C2
derived, HallC5×C9×C17 ⋊ C2×C13
HallC9×C13×C17 ⋊ D5
HallC5×C13×C17 ⋊ D9
HallC5×C9×C13 ⋊ D17
HallC13×C17 ⋊ D45
HallC9×C17 ⋊ D5×C13
HallC9×C13 ⋊ D85
HallC5×C17 ⋊ C13×D9
HallC5×C13 ⋊ D153
HallC5×C9 ⋊ C13×D17
SylowC17 ⋊ C13×D45
SylowC9 ⋊ C13×D85
SylowC5 ⋊ C13×D153

Subgroups

subgroupG/H
center, hypercenterC13D765
commutator, cosocle, hypocenterC5×C9×C17C2×C13
FrattiniC3C13×D255
FittingC5×C9×C13×C17C2
socleC3×C5×C13×C17D3
LCSG ▷ C5×C9×C17
UCSC1 ◁ C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9945

Conjugacy classes & character table

4992 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 15);