Finite Group Databasebeta

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D3×#41×AGL(1,𝔽11) #72217483

order10560
automorphism?
homologyAbelianization (H1) = C25×C5 · Schur multiplier (H2) = C29

Aliases

direct productD3×#41×AGL(1,𝔽11)

Splittings

FittingC3×C11×#41 ⋊ C22×C5
HallD3×#41×D11 ⋊ C5
HallC3×C11⋊C5 ⋊ C22×#41
HallC11⋊C5 ⋊ C2×D3×#41
HallC3×C11 ⋊ C22×C5×#41
SylowC11 ⋊ C2×C5×D3×#41
SylowC3 ⋊ C2×#41×AGL(1,𝔽11)

Subgroups

subgroupG/H
centerC4C22×D3×AGL(1,𝔽11)
commutator, socle, cosocleC2×C3×C11C25×C5
FrattiniC2C23×D3×AGL(1,𝔽11)
FittingC3×C11×#41C22×C5
hypercenter#41D3×AGL(1,𝔽11)
hypocenterC3×C11C22×C5×#41
LCSG ▷ C2×C3×C11 ▷ C3×C11
UCSC1 ◁ C4 ◁ #41

3560 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×AGL(1,ℤ/8)×AGL(1,𝔽11)
maximal normal subgroup ofD3×AGL(1,ℤ/8)×AGL(1,𝔽11)

GAP

Past the SmallGroups library coverage — no SmallGroups id.