Finite Group Databasebeta

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C22×C3×C49×C11⋊C5 #44568375

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C49 · Schur multiplier (H2) = C2

Aliases

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

Splittings

Fitting, HallC22×C3×C11×C49 ⋊ C5
derived, SylowC11 ⋊ C22×C3×C5×C49
HallC22×C11×C49 ⋊ C3×C5
HallC3×C11×C49 ⋊ C22×C5
HallC11×C49 ⋊ C22×C3×C5
HallC22×C3×C11 ⋊ C5×C49
HallC22×C11 ⋊ C3×C5×C49
HallC3×C11 ⋊ C22×C5×C49

Subgroups

subgroupG/H
center, hypercenterC22×C3×C49C11⋊C5
commutator, hypocenterC11C22×C3×C5×C49
FrattiniC7C22×C3×C7×C11⋊C5
FittingC22×C3×C11×C49C5
socleC22×C3×C7×C11C5×C7
prime radicalC22×C3×C7×C11⋊C5C7
cosocleC7×C11C22×C3×C5×C7
LCSG ▷ C11
UCSC1 ◁ C22×C3×C49

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6468

Conjugacy classes & character table

4116 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 77);