Finite Group Databasebeta

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A4×C49×C11⋊C5 #44568348

order32340
automorphism?
homologyAbelianization (H1) = C3×C5×C49 · Schur multiplier (H2) = C2

Aliases

direct productA4×C49×C11⋊C5
unambiguous semidirect productC22⋊(C3×C49×C11⋊C5)
unambiguous semidirect productC11⋊(C5×A4×C49)
unambiguous semidirect product(C11×A4)⋊(C5×C49)
unambiguous semidirect product(C22×C11⋊C5)⋊(C3×C49)
unambiguous semidirect product(C11×A4×C49)⋊C5

Splittings

Fitting, HallC22×C11×C49 ⋊ C3×C5
derived, HallC22×C11 ⋊ C3×C5×C49
HallC22×C49×C11⋊C5 ⋊ C3
HallC11×A4×C49 ⋊ C5
HallC11×C49 ⋊ C5×A4
HallC22×C11⋊C5 ⋊ C3×C49
HallC22×C49 ⋊ C3×C11⋊C5
HallC11×A4 ⋊ C5×C49
SylowC11 ⋊ C5×A4×C49
SylowC22 ⋊ C3×C49×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC49A4×C11⋊C5
commutator, hypocenterC22×C11C3×C5×C49
FrattiniC7C7×A4×C11⋊C5
FittingC22×C11×C49C3×C5
socle, cosocleC22×C7×C11C3×C5×C7
prime radicalC7×A4×C11⋊C5C7
LCSG ▷ C22×C11
UCSC1 ◁ C49

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2156

Conjugacy classes & character table

1372 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 50);