Finite Group Databasebeta

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C5×C13×D153 #34091026

order19890
automorphism?
homologyAbelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×D153
unambiguous semidirect productC9⋊(C5×C13×D17)
unambiguous semidirect productC17⋊(C5×C13×D9)

Splittings

Fitting, HallC5×C9×C13×C17 ⋊ C2
derived, HallC9×C17 ⋊ C2×C5×C13
HallC9×C13×C17 ⋊ C2×C5
HallC5×C13×C17 ⋊ D9
HallC5×C9×C17 ⋊ C2×C13
HallC5×C9×C13 ⋊ D17
HallC13×C17 ⋊ C5×D9
HallC9×C13 ⋊ C5×D17
HallC5×C17 ⋊ C13×D9
HallC5×C9 ⋊ C13×D17
SylowC17 ⋊ C5×C13×D9
SylowC9 ⋊ C5×C13×D17

Subgroups

subgroupG/H
center, hypercenterC5×C13D153
commutator, cosocle, hypocenterC9×C17C2×C5×C13
FrattiniC3C5×C13×D51
FittingC5×C9×C13×C17C2
socleC3×C5×C13×C17D3
LCSG ▷ C9×C17
UCSC1 ◁ C5×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9945

Conjugacy classes & character table

5070 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 11);