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C2×C13⋊C3×C3⋊AGL(1,𝔽11) #38788015

order25740
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13⋊C3×C3⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C3)⋊(C13⋊C3×AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊(D3×C13⋊C3)
unambiguous semidirect product(C2×D33)⋊(C5×C13⋊C3)
unambiguous semidirect product(C2×C13⋊C3×D33)⋊C5
unambiguous semidirect product(C2×C13×C3⋊AGL(1,𝔽11))⋊C3

Splittings

Fitting, socleC2×C3×C11×C13 ⋊ C2×C3×C5
derivedC3×C11×C13 ⋊ C22×C3×C5
HallC3×C13⋊C3×C11⋊C5 ⋊ C22
HallC2×C13⋊C3×D33 ⋊ C5
HallC3×C11×C13⋊C3 ⋊ C22×C5
HallC13×C11⋊C5 ⋊ C2×C3×D3
HallC11×C13 ⋊ C2×C3×C5×D3
HallC3×C13⋊C3 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×D3×C13⋊C3
SylowC13 ⋊ C2×C3×C3⋊AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D3×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C13⋊C3×C3⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C11×C13C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C13C2×C3×C5
LCSG ▷ C3×C11×C13
UCSC1 ◁ C2

176 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 54 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) = 858

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 246);