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C11×C3⋊(C3⋊#66775) #46778162

order33660
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C3

Aliases

direct productC11×C3⋊(C3⋊#66775)
unambiguous semidirect productC3⋊(C11×C3⋊#66775)

Splittings

Fitting, socle, HallC32×C5×C11×C17 ⋊ C4
derived, HallC32×C5×C17 ⋊ C4×C11
HallC32×C11×C17 ⋊ AGL(1,𝔽5)
HallC5×C11×C17 ⋊ C3⋊Dic3
HallC32×C5×C11 ⋊ #595
HallC11×C17 ⋊ C3⋊ΓL(1,𝔽16)
HallC32×C17 ⋊ C11×AGL(1,𝔽5)
HallC32×C11 ⋊ #66775
HallC5×C17 ⋊ C11×C3⋊Dic3
HallC5×C11 ⋊ C3⋊(C3⋊#595)
HallC32×C5 ⋊ C11×#595
SylowC17 ⋊ C11×C3⋊ΓL(1,𝔽16)
SylowC32 ⋊ C11×#66775
SylowC5 ⋊ C11×C3⋊(C3⋊#595)

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(C3⋊#66775)
commutator, hypocenterC32×C5×C17C4×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C17C4
prime radicalC32×C11×D85C2
cosocleC32×D85C2×C11
LCSG ▷ C32×C5×C17
UCSC1 ◁ C11

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8415

Conjugacy classes & character table

2211 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 330);