Finite Group Databasebeta

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C2×C11⋊C5×D49⋊C3 #44568338

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

Aliases

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

Splittings

FittingC2×C11×C49 ⋊ C2×C3×C5
derived, HallC11×C49 ⋊ C22×C3×C5
HallC2×C11⋊C5×D49 ⋊ C3
HallC11⋊C5×C49⋊C3 ⋊ C22
HallC2×C11×D49⋊C3 ⋊ C5
HallC49×C11⋊C5 ⋊ C22×C3
HallC2×C11×D49 ⋊ C3×C5
HallC11×C49⋊C3 ⋊ C22×C5
HallC2×D49 ⋊ C3×C11⋊C5
HallC49⋊C3 ⋊ C22×C11⋊C5
SylowC49 ⋊ C22×C3×C11⋊C5
SylowC11 ⋊ C2×C5×D49⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×D49⋊C3
commutator, cosocle, hypocenterC11×C49C22×C3×C5
FrattiniC7C2×AGL(1,𝔽7)×C11⋊C5
FittingC2×C11×C49C2×C3×C5
socleC2×C7×C11C5×AGL(1,𝔽7)
LCSG ▷ C11×C49
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1078

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 40);