Finite Group Databasebeta

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C2×C3×C5×D11×C49 #44568422

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

Aliases

direct productC2×C3×C5×D11×C49

Splittings

FittingC2×C3×C5×C11×C49 ⋊ C2
derived, SylowC11 ⋊ C22×C3×C5×C49
HallC3×C5×C11×C49 ⋊ C22
HallC5×C11×C49 ⋊ C22×C3
HallC3×C11×C49 ⋊ C22×C5
HallC11×C49 ⋊ C22×C3×C5
HallC3×C5×C11 ⋊ C22×C49
HallC5×C11 ⋊ C22×C3×C49
HallC3×C11 ⋊ C22×C5×C49

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C49D11
commutator, hypocenterC11C22×C3×C5×C49
FrattiniC7C2×C3×C5×C7×D11
FittingC2×C3×C5×C11×C49C2
socleC2×C3×C5×C7×C11C2×C7
prime radicalC2×C3×C5×C7×D11C7
cosocleC7×C11C22×C3×C5×C7
LCSG ▷ C11
UCSC1 ◁ C2×C3×C5×C49

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16170

Conjugacy classes & character table

10290 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 124);