Finite Group Databasebeta

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C7×Dic9×C11⋊C5 #28357356

order13860
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic9×C11⋊C5
unambiguous semidirect productC9⋊(C4×C7×C11⋊C5)
unambiguous semidirect product(C11×Dic9)⋊(C5×C7)
unambiguous semidirect product(C7×C11×Dic9)⋊C5

Splittings

derived, HallC9×C11 ⋊ C4×C5×C7
HallC7×C9×C11⋊C5 ⋊ C4
HallC7×C11×Dic9 ⋊ C5
HallC7×C9×C11 ⋊ C4×C5
HallC9×C11⋊C5 ⋊ C4×C7
HallC11×Dic9 ⋊ C5×C7
HallC7×C11 ⋊ C5×Dic9
HallC7×C9 ⋊ C4×C11⋊C5
SylowC11 ⋊ C5×C7×Dic9
SylowC9 ⋊ C4×C7×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C7D9×C11⋊C5
commutator, hypocenterC9×C11C4×C5×C7
FrattiniC2×C3D3×C7×C11⋊C5
FittingC2×C7×C9×C11C2×C5
socleC2×C3×C7×C11C5×D3
prime radicalC2×C3×C7×C11⋊C5D3
cosocleC2×C9×C11C2×C5×C7
LCSG ▷ C9×C11
UCSC1 ◁ C2×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2772

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 23);