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#127×C3⋊AGL(1,ℤ/9) #72219987

order5184
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C3×C4

Aliases

direct product#127×C3⋊AGL(1,ℤ/9)

Splittings

FittingC3×3−1+2×#127 ⋊ C2
SylowC3×3−1+2 ⋊ C2×#127

Subgroups

subgroupG/H
centerC22C23×C3⋊AGL(1,ℤ/9)
commutator, cosocleC22×C3×C9C24×C3
FrattiniC22×C3C23×C3×C3⋊D3
FittingC3×3−1+2×#127C2
socleC22×C32C23×C3×D3
hypercenter#127C3⋊AGL(1,ℤ/9)
hypocenterC3×C9C2×C3×#127
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ #127

5466 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup of#127×#92314, #72220090
maximal normal subgroup of#72220090
maximal quotient of#127×#92314

GAP

Past the SmallGroups library coverage — no SmallGroups id.