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M16×C3⋊AGL(1,𝔽11) #72216896

order5280
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22

Aliases

direct productM16×C3⋊AGL(1,𝔽11)

Splittings

FittingC3×C11×M16 ⋊ C2×C5
HallM16×D33 ⋊ C5
HallC3×C11⋊C5 ⋊ C2×M16
HallC11⋊C5 ⋊ D3×M16
HallC3×C11 ⋊ C2×C5×M16
SylowC11 ⋊ C5×D3×M16
SylowC3 ⋊ M16×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, FrattiniC4C22×C3⋊AGL(1,𝔽11)
commutator, socleC2×C3×C11C22×C4×C5
FittingC3×C11×M16C2×C5
prime radicalC22×C3⋊AGL(1,𝔽11)C4
cosocleC3×C4×C11C23×C5
hypercenterM16C3⋊AGL(1,𝔽11)
hypocenterC3×C11C2×C5×M16
LCSG ▷ C2×C3×C11 ▷ C3×C11
UCSC1 ◁ C4 ◁ M16

272 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×M16×AGL(1,𝔽11), AGL(1,ℤ/8)×C3⋊AGL(1,𝔽11), #72217327
maximal normal subgroup ofD3×M16×AGL(1,𝔽11), AGL(1,ℤ/8)×C3⋊AGL(1,𝔽11), #72217327

GAP

Past the SmallGroups library coverage — no SmallGroups id.