Finite Group Databasebeta

← Prev (#23780820) Next (#23780822) →

C3×A4×C289 #23780821

order10404
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C32×C289 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×A4×C289
unambiguous semidirect productC22⋊(C32×C289)
unambiguous semidirect product(C22×C3)⋊(C3×C289)
unambiguous semidirect product(C22×C289)⋊C32
unambiguous semidirect product(C22×C3×C289)⋊C3

Splittings

FittingC22×C3×C289 ⋊ C3
derived, SylowC22 ⋊ C32×C289
HallC22×C289 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C289A4
commutator, hypocenterC22C32×C289
FrattiniC17C3×A4×C17
FittingC22×C3×C289C3
socleC22×C3×C17C3×C17
prime radicalC3×A4×C17C17
cosocleC22×C17C32×C17
LCSG ▷ C22
UCSC1 ◁ C3×C289

42 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3468 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10404, 31);