Finite Group Databasebeta

← Prev (#37564675) Next (#37564677) →

C32×C49×C11⋊C5 #37564676

order24255
automorphism?
homologyAbelianization (H1) = C32×C5×C49 · Schur multiplier (H2) = C3

Aliases

direct productC32×C49×C11⋊C5
unambiguous semidirect productC11⋊(C32×C5×C49)
unambiguous semidirect product(C3×C11)⋊(C3×C5×C49)
unambiguous semidirect product(C32×C11)⋊(C5×C49)
unambiguous semidirect product(C32×C11×C49)⋊C5

Splittings

Fitting, HallC32×C11×C49 ⋊ C5
derived, SylowC11 ⋊ C32×C5×C49
HallC11×C49 ⋊ C32×C5
HallC32×C11 ⋊ C5×C49

Subgroups

subgroupG/H
center, hypercenterC32×C49C11⋊C5
commutator, hypocenterC11C32×C5×C49
FrattiniC7C32×C7×C11⋊C5
FittingC32×C11×C49C5
socleC32×C7×C11C5×C7
prime radicalC32×C7×C11⋊C5C7
cosocleC7×C11C32×C5×C7
LCSG ▷ C11
UCSC1 ◁ C32×C49

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4851

Conjugacy classes & character table

3087 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24255, 7);