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C2×Q8×AGL(1,𝔽11) #13183284

order1760
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C2×C5×Q8)
unambiguous semidirect product(C2×Q8×D11)⋊C5

Splittings

FittingC2×Q8×C11 ⋊ C2×C5
HallC2×Q8×D11 ⋊ C5
HallC11⋊C5 ⋊ C22×Q8
SylowC11 ⋊ C22×C5×Q8

Subgroups

subgroupG/H
centerC22C22×AGL(1,𝔽11)
commutator, cosocleC2×C11C24×C5
FrattiniC2C23×AGL(1,𝔽11)
FittingC2×Q8×C11C2×C5
socleC22×C11C23×C5
prime radicalC22×AGL(1,𝔽11)C22
hypercenterC2×Q8AGL(1,𝔽11)
hypocenterC11C22×C5×Q8
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×Q8

312 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 176

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×Q8×AGL(1,𝔽11), C2×SD16×AGL(1,𝔽11), C2×#41×AGL(1,𝔽11), …
maximal normal subgroup ofC2×SD16×AGL(1,𝔽11), C2×#41×AGL(1,𝔽11), C22⋊Q8×AGL(1,𝔽11), …
maximal quotient ofD3×Q8×AGL(1,𝔽11), C22⋊Q8×AGL(1,𝔽11), C4⋊Q8×AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 1093);