Finite Group Databasebeta

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C7×D17×D13⋊C3 #32915460

order18564
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D17×D13⋊C3
unambiguous semidirect productD13⋊(C3×C7×D17)
unambiguous semidirect product(D13×D17)⋊(C3×C7)
unambiguous semidirect product(D17×C13⋊C3)⋊(C2×C7)
unambiguous semidirect product(C17×D13⋊C3)⋊(C2×C7)
unambiguous semidirect product(C17⋊(D13⋊C3))⋊(C2×C7)

Splittings

Fitting, socle, HallC7×C13×C17 ⋊ C22×C3
derived, HallC13×C17 ⋊ C22×C3×C7
HallC7×D13×D17 ⋊ C3
HallC7×C17×C13⋊C3 ⋊ C22
HallD13×D17 ⋊ C3×C7
HallC17×C13⋊C3 ⋊ C22×C7
HallC7×C13⋊C3 ⋊ C2×D17
HallC7×C17 ⋊ C2×D13⋊C3
HallC7×C13 ⋊ C2×C3×D17
HallC13⋊C3 ⋊ C2×C7×D17
SylowC17 ⋊ C2×C7×D13⋊C3
SylowC13 ⋊ C2×C3×C7×D17

Subgroups

subgroupG/H
center, hypercenterC7D17×D13⋊C3
commutator, cosocle, hypocenterC13×C17C22×C3×C7
FrattiniC1G
Fitting, socleC7×C13×C17C22×C3
LCSG ▷ C13×C17
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1547

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 55);