Finite Group Databasebeta

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C5×C11×A4×C49 #44568420

order32340
automorphism?
homologyAbelianization (H1) = C3×C5×C11×C49 · Schur multiplier (H2) = C2

Aliases

direct productC5×C11×A4×C49
unambiguous semidirect productC22⋊(C3×C5×C11×C49)
unambiguous semidirect product(C22×C5)⋊(C3×C11×C49)
unambiguous semidirect product(C22×C5×C11)⋊(C3×C49)

Splittings

Fitting, HallC22×C5×C11×C49 ⋊ C3
derived, SylowC22 ⋊ C3×C5×C11×C49
HallC22×C11×C49 ⋊ C3×C5
HallC22×C5×C49 ⋊ C3×C11
HallC22×C5×C11 ⋊ C3×C49
HallC22×C49 ⋊ C3×C5×C11
HallC22×C11 ⋊ C3×C5×C49
HallC22×C5 ⋊ C3×C11×C49

Subgroups

subgroupG/H
center, hypercenterC5×C11×C49A4
commutator, hypocenterC22C3×C5×C11×C49
FrattiniC7C5×C7×C11×A4
FittingC22×C5×C11×C49C3
socleC22×C5×C7×C11C3×C7
prime radicalC5×C7×C11×A4C7
cosocleC22×C7C3×C5×C7×C11
LCSG ▷ C22
UCSC1 ◁ C5×C11×C49

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10780

Conjugacy classes & character table

10780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 122);