Finite Group Databasebeta

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C2×C9×D7×C11⋊C5 #28357398

order13860
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D7×C11⋊C5
unambiguous semidirect product(C2×C9×C11×D7)⋊C5

Splittings

FittingC2×C7×C9×C11 ⋊ C2×C5
derived, HallC7×C11 ⋊ C22×C5×C9
HallC7×C9×C11⋊C5 ⋊ C22
HallC2×C9×C11×D7 ⋊ C5
HallC7×C9×C11 ⋊ C22×C5
HallC7×C11⋊C5 ⋊ C22×C9
HallC2×C11×D7 ⋊ C5×C9
HallC9×C11 ⋊ C2×C5×D7
HallC7×C9 ⋊ C22×C11⋊C5
SylowC11 ⋊ C2×C5×C9×D7
SylowC7 ⋊ C22×C9×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C9D7×C11⋊C5
commutator, hypocenterC7×C11C22×C5×C9
FrattiniC3C2×C3×D7×C11⋊C5
FittingC2×C7×C9×C11C2×C5
socleC2×C3×C7×C11C2×C3×C5
prime radicalC2×C3×D7×C11⋊C5C3
cosocleC3×C7×C11C22×C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C9

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1386

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 65);