Finite Group Databasebeta

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C2×C7×C9×D143 #49114518

order36036
automorphism?
homologyAbelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×C9×D143
unambiguous semidirect product(C2×C11)⋊(C7×C9×D13)

Splittings

FittingC2×C7×C9×C11×C13 ⋊ C2
derived, HallC11×C13 ⋊ C22×C7×C9
HallC7×C9×C11×C13 ⋊ C22
HallC9×C11×C13 ⋊ C22×C7
HallC7×C11×C13 ⋊ C22×C9
HallC7×C9×C13 ⋊ C2×D11
HallC7×C9×C11 ⋊ C2×D13
HallC9×C13 ⋊ C2×C7×D11
HallC9×C11 ⋊ C2×C7×D13
HallC7×C13 ⋊ C2×C9×D11
HallC7×C11 ⋊ C2×C9×D13
SylowC13 ⋊ C2×C7×C9×D11
SylowC11 ⋊ C2×C7×C9×D13

Subgroups

subgroupG/H
center, hypercenterC2×C7×C9D143
commutator, hypocenterC11×C13C22×C7×C9
FrattiniC3C2×C3×C7×D143
FittingC2×C7×C9×C11×C13C2
socleC2×C3×C7×C11×C13C2×C3
prime radicalC2×C3×C7×D143C3
cosocleC3×C11×C13C22×C3×C7
LCSG ▷ C11×C13
UCSC1 ◁ C2×C7×C9

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18018

Conjugacy classes & character table

9198 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 186);