Finite Group Databasebeta

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C32×C11⋊#66772 #46778071

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

Aliases

direct productC32×C11⋊#66772
unambiguous semidirect productC11⋊(C32×#66772)

Splittings

Fitting, socle, HallC32×C5×C11×C17 ⋊ C4
derived, HallC5×C11×C17 ⋊ C32×C4
HallC32×C11×C17 ⋊ Dic5
HallC32×C5×C17 ⋊ Dic11
HallC32×C5×C11 ⋊ #595
HallC11×C17 ⋊ C32×Dic5
HallC32×C17 ⋊ Dic55
HallC32×C11 ⋊ #66772
HallC5×C17 ⋊ C32×Dic11
HallC5×C11 ⋊ C32×#595
HallC32×C5 ⋊ C11⋊#595
SylowC17 ⋊ C32×Dic55
SylowC11 ⋊ C32×#66772
SylowC5 ⋊ C32×C11⋊#595

Subgroups

subgroupG/H
center, hypercenterC32C11⋊#66772
commutator, hypocenterC5×C11×C17C32×C4
FrattiniC1G
Fitting, socleC32×C5×C11×C17C4
prime radicalC32×C5×C11×D17C2
cosocleC5×C11×D17C2×C32
LCSG ▷ C5×C11×C17
UCSC1 ◁ C32

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8415

Conjugacy classes & character table

2502 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 239);