Finite Group Databasebeta

← Prev (#46778057) Next (#46778059) →

C32×C5×C11×#595 #46778058

order33660
automorphism?
homologyAbelianization (H1) = C32×C4×C5×C11 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×C11×#595

Splittings

Fitting, socle, HallC32×C5×C11×C17 ⋊ C4
derived, SylowC17 ⋊ C32×C4×C5×C11
HallC32×C11×C17 ⋊ C4×C5
HallC5×C11×C17 ⋊ C32×C4
HallC32×C5×C17 ⋊ C4×C11
HallC11×C17 ⋊ C32×C4×C5
HallC32×C17 ⋊ C4×C5×C11
HallC5×C17 ⋊ C32×C4×C11

Subgroups

subgroupG/H
center, hypercenterC32×C5×C11#595
commutator, hypocenterC17C32×C4×C5×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C17C4
prime radicalC32×C5×C11×D17C2
cosocleD17C2×C32×C5×C11
LCSG ▷ C17
UCSC1 ◁ C32×C5×C11

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8415

Conjugacy classes & character table

3960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 226);