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C9×(C11⋊C5)⋊Dic17 #46777852

order33660
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×(C11⋊C5)⋊Dic17
unambiguous semidirect product(C11⋊C5)⋊(C9×Dic17)
unambiguous semidirect productDic187⋊(C5×C9)
unambiguous semidirect product(C9×Dic187)⋊C5

Splittings

derived, HallC11×C17 ⋊ C4×C5×C9
HallC9×C17×C11⋊C5 ⋊ C4
HallC9×Dic187 ⋊ C5
HallC9×C11×C17 ⋊ C4×C5
HallC17×C11⋊C5 ⋊ C4×C9
HallDic187 ⋊ C5×C9
HallC9×C11⋊C5 ⋊ Dic17
HallC9×C17 ⋊ Dic11⋊C5
HallC9×C11 ⋊ C5×Dic17
HallC11⋊C5 ⋊ C9×Dic17
SylowC17 ⋊ C9×Dic11⋊C5
SylowC11 ⋊ C5×C9×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C9C17⋊AGL(1,𝔽11)
commutator, hypocenterC11×C17C4×C5×C9
FrattiniC2×C3C3×C17⋊AGL(1,𝔽11)
FittingC2×C9×C11×C17C2×C5
socle, cosocleC2×C3×C11×C17C2×C3×C5
prime radicalC2×C3×C17×C11⋊C5C2×C3
LCSG ▷ C11×C17
UCSC1 ◁ C2×C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6732

Conjugacy classes & character table

1206 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 20);