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C5×D1989 #34091028

order19890
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D1989
unambiguous semidirect productC9⋊(C5×D221)
unambiguous semidirect productC13⋊(C5×D153)
unambiguous semidirect productC17⋊(C5×D117)

Splittings

Fitting, HallC5×C9×C13×C17 ⋊ C2
derived, HallC9×C13×C17 ⋊ C2×C5
HallC5×C13×C17 ⋊ D9
HallC5×C9×C17 ⋊ D13
HallC5×C9×C13 ⋊ D17
HallC13×C17 ⋊ C5×D9
HallC9×C17 ⋊ C5×D13
HallC9×C13 ⋊ C5×D17
HallC5×C17 ⋊ D117
HallC5×C13 ⋊ D153
HallC5×C9 ⋊ D221
SylowC17 ⋊ C5×D117
SylowC13 ⋊ C5×D153
SylowC9 ⋊ C5×D221

Subgroups

subgroupG/H
center, hypercenterC5D1989
commutator, cosocle, hypocenterC9×C13×C17C2×C5
FrattiniC3C5×D663
FittingC5×C9×C13×C17C2
socleC3×C5×C13×C17D3
LCSG ▷ C9×C13×C17
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9945

Conjugacy classes & character table

4980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 13);