Finite Group Databasebeta

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C2×C5×C17×C13⋊C9 #34091017

order19890
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C17 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C17×C13⋊C9
unambiguous semidirect product(C2×C13)⋊(C5×C9×C17)
unambiguous semidirect product(C2×C5×C13)⋊(C9×C17)
unambiguous semidirect product(C2×C13×C17)⋊(C5×C9)
unambiguous semidirect product(C2×C5×C13×C17)⋊C9

Splittings

derived, SylowC13 ⋊ C2×C5×C9×C17
HallC2×C5×C13×C17 ⋊ C9
HallC5×C13×C17 ⋊ C2×C9
HallC2×C13×C17 ⋊ C5×C9
HallC13×C17 ⋊ C2×C5×C9
HallC2×C5×C13 ⋊ C9×C17
HallC5×C13 ⋊ C2×C9×C17
HallC2×C13 ⋊ C5×C9×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C17C13⋊C3
commutator, hypocenterC13C2×C5×C9×C17
FrattiniC3C2×C5×C17×C13⋊C3
Fitting, socle, prime radicalC2×C3×C5×C13×C17C3
cosocleC3×C13C2×C3×C5×C17
LCSG ▷ C13
UCSC1 ◁ C2×C3×C5×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19890

Conjugacy classes & character table

3570 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 2);