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C17×C9⋊(C11⋊AGL(1,𝔽5)) #46777909

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

Aliases

direct productC17×C9⋊(C11⋊AGL(1,𝔽5))
unambiguous semidirect productC9⋊(C17×C11⋊AGL(1,𝔽5))
unambiguous semidirect productC11⋊(C17×C9⋊AGL(1,𝔽5))

Splittings

Fitting, HallC5×C9×C11×C17 ⋊ C4
derived, HallC5×C9×C11 ⋊ C4×C17
HallC9×C11×C17 ⋊ AGL(1,𝔽5)
HallC5×C11×C17 ⋊ Dic9
HallC5×C9×C17 ⋊ Dic11
HallC11×C17 ⋊ C9⋊AGL(1,𝔽5)
HallC9×C17 ⋊ C11⋊AGL(1,𝔽5)
HallC9×C11 ⋊ C17×AGL(1,𝔽5)
HallC5×C17 ⋊ Dic99
HallC5×C11 ⋊ C17×Dic9
HallC5×C9 ⋊ C17×Dic11
SylowC11 ⋊ C17×C9⋊AGL(1,𝔽5)
SylowC9 ⋊ C17×C11⋊AGL(1,𝔽5)
SylowC5 ⋊ C17×Dic99

Subgroups

subgroupG/H
center, hypercenterC17C9⋊(C11⋊AGL(1,𝔽5))
commutator, hypocenterC5×C9×C11C4×C17
FrattiniC3C17×C3⋊(C11⋊AGL(1,𝔽5))
FittingC5×C9×C11×C17C4
socleC3×C5×C11×C17Dic3
prime radicalC3×D5×C11×C17D3
cosocleC9×D5×C11C2×C17
LCSG ▷ C5×C9×C11
UCSC1 ◁ C17

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8415

Conjugacy classes & character table

3417 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 77);