Finite Group Databasebeta

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C2×C3×C5×C17×C13⋊C3 #34091056

order19890
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C17 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C5×C17×C13⋊C3
unambiguous semidirect product(C2×C13)⋊(C32×C5×C17)
unambiguous semidirect product(C2×C3×C13)⋊(C3×C5×C17)
unambiguous semidirect product(C2×C5×C13)⋊(C32×C17)
unambiguous semidirect product(C2×C3×C5×C13)⋊(C3×C17)
unambiguous semidirect product(C2×C13×C17)⋊(C32×C5)
unambiguous semidirect product(C2×C3×C13×C17)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C13×C17)⋊C32
unambiguous semidirect product(C2×C3×C5×C13×C17)⋊C3

Splittings

Fitting, socleC2×C3×C5×C13×C17 ⋊ C3
derived, SylowC13 ⋊ C2×C32×C5×C17
HallC2×C5×C13×C17 ⋊ C32
HallC5×C13×C17 ⋊ C2×C32
HallC2×C13×C17 ⋊ C32×C5
HallC13×C17 ⋊ C2×C32×C5
HallC2×C5×C13 ⋊ C32×C17
HallC5×C13 ⋊ C2×C32×C17
HallC2×C13 ⋊ C32×C5×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C17C13⋊C3
commutator, cosocle, hypocenterC13C2×C32×C5×C17
FrattiniC1G
Fitting, socleC2×C3×C5×C13×C17C3
LCSG ▷ C13
UCSC1 ◁ C2×C3×C5×C17

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6630

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, 41);