Finite Group Databasebeta

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C32×C11⋊#66774 #46778068

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

Aliases

direct productC32×C11⋊#66774
unambiguous semidirect productC11⋊(C32×#66774)

Splittings

Fitting, socle, HallC32×C5×C11×C17 ⋊ C4
derived, HallC5×C11×C17 ⋊ C32×C4
HallC32×C11×C17 ⋊ AGL(1,𝔽5)
HallC32×C5×C17 ⋊ Dic11
HallC32×C5×C11 ⋊ Dic17
HallC11×C17 ⋊ C32×AGL(1,𝔽5)
HallC32×C17 ⋊ C11⋊AGL(1,𝔽5)
HallC32×C11 ⋊ #66774
HallC5×C17 ⋊ C32×Dic11
HallC5×C11 ⋊ C32×Dic17
HallC32×C5 ⋊ Dic187
SylowC17 ⋊ C32×C11⋊AGL(1,𝔽5)
SylowC11 ⋊ C32×#66774
SylowC5 ⋊ C32×Dic187

Subgroups

subgroupG/H
center, hypercenterC32C11⋊#66774
commutator, hypocenterC5×C11×C17C32×C4
FrattiniC1G
Fitting, socleC32×C5×C11×C17C4
prime radicalC32×D5×C11×C17C2
cosocleD5×C11×C17C2×C32
LCSG ▷ C5×C11×C17
UCSC1 ◁ C32

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8415

Conjugacy classes & character table

3393 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 236);