Finite Group Databasebeta

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C2×C5×C11×D49⋊C3 #44568368

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C11×D49⋊C3
unambiguous semidirect productD49⋊(C2×C3×C5×C11)
unambiguous semidirect product(C49⋊C3)⋊(C22×C5×C11)
unambiguous semidirect product(C2×D49)⋊(C3×C5×C11)
unambiguous semidirect product(C2×C49⋊C3)⋊(C2×C5×C11)
unambiguous semidirect product(C2×C5×D49)⋊(C3×C11)
unambiguous semidirect product(C2×C5×C11×D49)⋊C3

Splittings

FittingC2×C5×C11×C49 ⋊ C2×C3
derived, SylowC49 ⋊ C22×C3×C5×C11
HallC2×C5×C11×D49 ⋊ C3
HallC5×C11×C49⋊C3 ⋊ C22
HallC5×C11×C49 ⋊ C22×C3
HallC2×C11×D49 ⋊ C3×C5
HallC11×C49⋊C3 ⋊ C22×C5
HallC2×C5×D49 ⋊ C3×C11
HallC5×C49⋊C3 ⋊ C22×C11
HallC11×C49 ⋊ C22×C3×C5
HallC5×C49 ⋊ C22×C3×C11
HallC2×D49 ⋊ C3×C5×C11
HallC49⋊C3 ⋊ C22×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D49⋊C3
commutator, cosocle, hypocenterC49C22×C3×C5×C11
FrattiniC7C2×C5×C11×AGL(1,𝔽7)
FittingC2×C5×C11×C49C2×C3
socleC2×C5×C7×C11AGL(1,𝔽7)
LCSG ▷ C49
UCSC1 ◁ C2×C5×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5390

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 70);