Finite Group Databasebeta

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C4×C7×C9×C11⋊C5 #28357335

order13860
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C4×C5×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7×C9×C11⋊C5
unambiguous semidirect product(C4×C11)⋊(C5×C7×C9)
unambiguous semidirect product(C4×C9×C11)⋊(C5×C7)
unambiguous semidirect product(C4×C7×C9×C11)⋊C5

Splittings

Fitting, HallC4×C7×C9×C11 ⋊ C5
derived, SylowC11 ⋊ C4×C5×C7×C9
HallC7×C9×C11 ⋊ C4×C5
HallC4×C9×C11 ⋊ C5×C7
HallC4×C7×C11 ⋊ C5×C9
HallC9×C11 ⋊ C4×C5×C7
HallC7×C11 ⋊ C4×C5×C9
HallC4×C11 ⋊ C5×C7×C9

Subgroups

subgroupG/H
center, hypercenterC4×C7×C9C11⋊C5
commutator, hypocenterC11C4×C5×C7×C9
FrattiniC2×C3C2×C3×C7×C11⋊C5
FittingC4×C7×C9×C11C5
socleC2×C3×C7×C11C2×C3×C5
prime radicalC2×C3×C7×C11⋊C5C2×C3
cosocleC2×C3×C11C2×C3×C5×C7
LCSG ▷ C11
UCSC1 ◁ C4×C7×C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2772

Conjugacy classes & character table

1764 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 2);