Finite Group Databasebeta

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C17×C9⋊(Dic11⋊C5) #46777855

order33660
automorphism?
homologyAbelianization (H1) = C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×C9⋊(Dic11⋊C5)
unambiguous semidirect productC9⋊(C17×Dic11⋊C5)
unambiguous semidirect product(C11⋊C5)⋊(C17×Dic9)
unambiguous semidirect productDic99⋊(C5×C17)
unambiguous semidirect product(C17×Dic99)⋊C5

Splittings

derived, HallC9×C11 ⋊ C4×C5×C17
HallC9×C17×C11⋊C5 ⋊ C4
HallC17×Dic99 ⋊ C5
HallC9×C11×C17 ⋊ C4×C5
HallC17×C11⋊C5 ⋊ Dic9
HallC9×C11⋊C5 ⋊ C4×C17
HallDic99 ⋊ C5×C17
HallC11×C17 ⋊ C5×Dic9
HallC9×C17 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C17×Dic9
SylowC11 ⋊ C5×C17×Dic9
SylowC9 ⋊ C17×Dic11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C17C9⋊AGL(1,𝔽11)
commutator, hypocenterC9×C11C4×C5×C17
FrattiniC2×C3C17×C3⋊AGL(1,𝔽11)
FittingC2×C9×C11×C17C2×C5
socleC2×C3×C11×C17C5×D3
prime radicalC2×C3×C17×C11⋊C5D3
cosocleC2×C9×C11C2×C5×C17
LCSG ▷ C9×C11
UCSC1 ◁ C2×C17

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6732

Conjugacy classes & character table

1326 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 23);