Finite Group Databasebeta

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C32×C11×#66774 #46778064

order33660
automorphism?
homologyAbelianization (H1) = C32×C4×C11 · Schur multiplier (H2) = C3

Aliases

direct productC32×C11×#66774

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC32×C11#66774
commutator, hypocenterC5×C17C32×C4×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C17C4
prime radicalC32×D5×C11×C17C2
cosocleD5×C17C2×C32×C11
LCSG ▷ C5×C17
UCSC1 ◁ C32×C11

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8415

Conjugacy classes & character table

3663 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 232);