Finite Group Databasebeta

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C2×C9×C11×D71 #43244666

order28116
automorphism?
homologyAbelianization (H1) = C22×C9×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×C11×D71
unambiguous semidirect productC71⋊(C22×C9×C11)
unambiguous semidirect product(C2×C71)⋊(C2×C9×C11)

Splittings

FittingC2×C9×C11×C71 ⋊ C2
derived, SylowC71 ⋊ C22×C9×C11
HallC9×C11×C71 ⋊ C22
HallC11×C71 ⋊ C22×C9
HallC9×C71 ⋊ C22×C11

Subgroups

subgroupG/H
center, hypercenterC2×C9×C11D71
commutator, hypocenterC71C22×C9×C11
FrattiniC3C2×C3×C11×D71
FittingC2×C9×C11×C71C2
socleC2×C3×C11×C71C2×C3
prime radicalC2×C3×C11×D71C3
cosocleC3×C71C22×C3×C11
LCSG ▷ C71
UCSC1 ◁ C2×C9×C11

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14058

Conjugacy classes & character table

7326 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28116, 24);