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C4⋊(C3⋊AGL(1,𝔽11)) #13050331

order1320
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productC4⋊(C3⋊AGL(1,𝔽11))
unambiguous semidirect productD132⋊C5

Splittings

FittingC3×C4×C11 ⋊ C2×C5
HallD132 ⋊ C5
HallC3×C11⋊C5 ⋊ D4
HallC11⋊C5 ⋊ D12
HallC3×C11 ⋊ C5×D4
SylowC11 ⋊ C5×D12
SylowC3 ⋊ C4⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, FrattiniC2C2×C3⋊AGL(1,𝔽11)
commutator, socle, cosocleC2×C3×C11C22×C5
FittingC3×C4×C11C2×C5
hypercenterC4C3⋊AGL(1,𝔽11)
hypocenterC3×C11C5×D4
LCSG ▷ C2×C3×C11 ▷ C3×C11
UCSC1 ◁ C2 ◁ C4

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 132

Polycyclic presentation:

2^2,5,2,3,11|b^2=d,b^a=bd,e^a=e^2,f^a=f^10,f^c=f^5

Conjugacy classes & character table

57 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD4×C3⋊AGL(1,𝔽11), D3×C4⋊AGL(1,𝔽11), D12×AGL(1,𝔽11), …
maximal normal subgroup ofD4×C3⋊AGL(1,𝔽11), D3×C4⋊AGL(1,𝔽11), D12×AGL(1,𝔽11), …
maximal quotient ofC2×C4⋊(C3⋊AGL(1,𝔽11)), #72216781, #72216791, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 35);