Finite Group Databasebeta

← Prev (#28357552) Next (#28357554) →

C3×D21⋊AGL(1,𝔽11) #28357553

order13860
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC3×D21⋊AGL(1,𝔽11)
unambiguous semidirect product(C3⋊AGL(1,𝔽11))⋊(C3×D7)
unambiguous semidirect product(C3×D21⋊D11)⋊C5

Splittings

Fitting, socle, HallC32×C7×C11 ⋊ C22×C5
derivedC3×C7×C11 ⋊ C22×C3×C5
HallC32×C7×C11⋊C5 ⋊ C22
HallC3×D21⋊D11 ⋊ C5
HallC32×C11⋊C5 ⋊ C2×D7
HallC7×C11⋊C5 ⋊ C2×C3×D3
HallC32×C11 ⋊ C2×C5×D7
HallC7×C11 ⋊ C2×C3×C5×D3
HallC32×C7 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C3×D3×D7
SylowC11 ⋊ C3×C5×D3×D7
SylowC32 ⋊ D7×AGL(1,𝔽11)
SylowC7 ⋊ C3×D3×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC3D21⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C7×C11C22×C3×C5
FrattiniC1G
Fitting, socleC32×C7×C11C22×C5
LCSG ▷ C3×C7×C11
UCSC1 ◁ C3

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 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) = 462

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 220);