Finite Group Databasebeta

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C2×C7×C17×D13⋊C3 #32915531

order18564
automorphism?
homologyAbelianization (H1) = C22×C3×C7×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×C17×D13⋊C3
unambiguous semidirect productD13⋊(C2×C3×C7×C17)
unambiguous semidirect product(C13⋊C3)⋊(C22×C7×C17)
unambiguous semidirect product(C2×D13)⋊(C3×C7×C17)
unambiguous semidirect product(C2×C13⋊C3)⋊(C2×C7×C17)
unambiguous semidirect product(C2×C17×D13)⋊(C3×C7)

Splittings

Fitting, socleC2×C7×C13×C17 ⋊ C2×C3
derived, SylowC13 ⋊ C22×C3×C7×C17
HallC2×C7×C17×D13 ⋊ C3
HallC7×C17×C13⋊C3 ⋊ C22
HallC7×C13×C17 ⋊ C22×C3
HallC2×C17×D13 ⋊ C3×C7
HallC17×C13⋊C3 ⋊ C22×C7
HallC2×C7×D13 ⋊ C3×C17
HallC7×C13⋊C3 ⋊ C22×C17
HallC13×C17 ⋊ C22×C3×C7
HallC7×C13 ⋊ C22×C3×C17
HallC2×D13 ⋊ C3×C7×C17
HallC13⋊C3 ⋊ C22×C7×C17

Subgroups

subgroupG/H
center, hypercenterC2×C7×C17D13⋊C3
commutator, cosocle, hypocenterC13C22×C3×C7×C17
FrattiniC1G
Fitting, socleC2×C7×C13×C17C2×C3
LCSG ▷ C13
UCSC1 ◁ C2×C7×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3094

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 126);