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C32×C17×C11⋊AGL(1,𝔽5) #46778065

order33660
automorphism?
homologyAbelianization (H1) = C32×C4×C17 · Schur multiplier (H2) = C3

Aliases

direct productC32×C17×C11⋊AGL(1,𝔽5)
unambiguous semidirect productC11⋊(C32×C17×AGL(1,𝔽5))

Splittings

Fitting, socle, HallC32×C5×C11×C17 ⋊ C4
derived, HallC5×C11 ⋊ C32×C4×C17
HallC32×C11×C17 ⋊ AGL(1,𝔽5)
HallC5×C11×C17 ⋊ C32×C4
HallC32×C5×C17 ⋊ Dic11
HallC32×C5×C11 ⋊ C4×C17
HallC11×C17 ⋊ C32×AGL(1,𝔽5)
HallC32×C11 ⋊ C17×AGL(1,𝔽5)
HallC5×C17 ⋊ C32×Dic11
HallC32×C5 ⋊ C17×Dic11
SylowC11 ⋊ C32×C17×AGL(1,𝔽5)
SylowC5 ⋊ C32×C17×Dic11

Subgroups

subgroupG/H
center, hypercenterC32×C17C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C32×C4×C17
FrattiniC1G
Fitting, socleC32×C5×C11×C17C4
prime radicalC32×D5×C11×C17C2
cosocleD5×C11C2×C32×C17
LCSG ▷ C5×C11
UCSC1 ◁ C32×C17

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8415

Conjugacy classes & character table

3825 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 233);