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C3×D13×AGL(1,𝔽11) #22575073

order8580
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC3×D13×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C3×C5×D13)
unambiguous semidirect product(C3×D11×D13)⋊C5

Splittings

Fitting, socle, HallC3×C11×C13 ⋊ C22×C5
derived, HallC11×C13 ⋊ C22×C3×C5
HallC3×C13×C11⋊C5 ⋊ C22
HallC3×D11×D13 ⋊ C5
HallC13×C11⋊C5 ⋊ C22×C3
HallD11×D13 ⋊ C3×C5
HallC3×C11⋊C5 ⋊ C2×D13
HallC11⋊C5 ⋊ C2×C3×D13
HallC3×C13 ⋊ C2×AGL(1,𝔽11)
HallC3×C11 ⋊ C2×C5×D13
SylowC13 ⋊ C2×C3×AGL(1,𝔽11)
SylowC11 ⋊ C2×C3×C5×D13

Subgroups

subgroupG/H
center, hypercenterC3D13×AGL(1,𝔽11)
commutator, hypocenterC11×C13C22×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C13C22×C5
LCSG ▷ C11×C13
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

264 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×D13⋊C9, C9×D13×AGL(1,𝔽11), C3×D13⋊C3×AGL(1,𝔽11), …
maximal normal subgroup ofAGL(1,𝔽11)×D13⋊C9, C9×D13×AGL(1,𝔽11), C3×D13⋊C3×AGL(1,𝔽11), …
maximal quotient ofC9×D13×AGL(1,𝔽11), C32×D13×AGL(1,𝔽11), C3×D13×C3⋊AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 45);