Finite Group Databasebeta

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C3×D49×AGL(1,𝔽11) #44568340

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

Aliases

direct productC3×D49×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C3×C5×D49)
unambiguous semidirect product(C3×D11×D49)⋊C5

Splittings

Fitting, HallC3×C11×C49 ⋊ C22×C5
derived, HallC11×C49 ⋊ C22×C3×C5
HallC3×C49×C11⋊C5 ⋊ C22
HallC3×D11×D49 ⋊ C5
HallC49×C11⋊C5 ⋊ C22×C3
HallD11×D49 ⋊ C3×C5
HallC3×C11⋊C5 ⋊ C2×D49
HallC3×C49 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×C3×D49
SylowC49 ⋊ C2×C3×AGL(1,𝔽11)
HallC3×C11 ⋊ C2×C5×D49
SylowC11 ⋊ C2×C3×C5×D49

Subgroups

subgroupG/H
center, hypercenterC3D49×AGL(1,𝔽11)
commutator, cosocle, hypocenterC11×C49C22×C3×C5
FrattiniC7C3×D7×AGL(1,𝔽11)
FittingC3×C11×C49C22×C5
socleC3×C7×C11C2×C5×D7
LCSG ▷ C11×C49
UCSC1 ◁ C3

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1617

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 42);