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C17×C11⋊#4380 #46778048

order33660
automorphism?
homologyAbelianization (H1) = C4×C17 · Schur multiplier (H2) = C3

Aliases

direct productC17×C11⋊#4380
unambiguous semidirect productC11⋊(C17×#4380)

Splittings

Fitting, socle, HallC32×C5×C11×C17 ⋊ C4
derived, HallC32×C5×C11 ⋊ C4×C17
HallC32×C11×C17 ⋊ AGL(1,𝔽5)
HallC5×C11×C17 ⋊ #157
HallC32×C5×C17 ⋊ Dic11
HallC11×C17 ⋊ #4380
HallC32×C17 ⋊ C11⋊AGL(1,𝔽5)
HallC32×C11 ⋊ C17×AGL(1,𝔽5)
HallC5×C17 ⋊ C11⋊#157
HallC5×C11 ⋊ C17×#157
HallC32×C5 ⋊ C17×Dic11
SylowC11 ⋊ C17×#4380
SylowC32 ⋊ C17×C11⋊AGL(1,𝔽5)
SylowC5 ⋊ C17×C11⋊#157

Subgroups

subgroupG/H
center, hypercenterC17C11⋊#4380
commutator, hypocenterC32×C5×C11C4×C17
FrattiniC1G
Fitting, socleC32×C5×C11×C17C4
prime radicalC11×C17×C3⋊D15C2
cosocleC11×C3⋊D15C2×C17
LCSG ▷ C32×C5×C11
UCSC1 ◁ C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5610

Conjugacy classes & character table

2295 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 216);