Finite Group Databasebeta

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C2×C5×D11×C49⋊C3 #44568370

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

Aliases

direct productC2×C5×D11×C49⋊C3
unambiguous semidirect product(C2×C5×D11×C49)⋊C3

Splittings

FittingC2×C5×C11×C49 ⋊ C2×C3
derived, HallC11×C49 ⋊ C22×C3×C5
HallC2×C5×D11×C49 ⋊ C3
HallC5×C11×C49⋊C3 ⋊ C22
HallC5×C11×C49 ⋊ C22×C3
HallC2×D11×C49 ⋊ C3×C5
HallC11×C49⋊C3 ⋊ C22×C5
HallC5×C49 ⋊ C2×C3×D11
HallC5×C11 ⋊ C22×C49⋊C3
SylowC49 ⋊ C2×C3×C5×D11
SylowC11 ⋊ C22×C5×C49⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5D11×C49⋊C3
commutator, cosocle, hypocenterC11×C49C22×C3×C5
FrattiniC7C2×C5×ΓL(1,𝔽8)×D11
FittingC2×C5×C11×C49C2×C3
socleC2×C5×C7×C11C2×ΓL(1,𝔽8)
LCSG ▷ C11×C49
UCSC1 ◁ C2×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5390

Conjugacy classes & character table

1330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 72);