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D3×ΓL(1,𝔽8)×#127 #72244249

order4032
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C4

Aliases

direct productD3×ΓL(1,𝔽8)×#127

Splittings

FittingC3×C7×#127 ⋊ C2×C3
HallC3×ΓL(1,𝔽8) ⋊ C2×#127
SylowC7 ⋊ C3×D3×#127

Subgroups

subgroupG/H
center, FrattiniC22C23×D3×ΓL(1,𝔽8)
commutator, socle, cosocleC22×C3×C7C24×C3
FittingC3×C7×#127C2×C3
hypercenter#127D3×ΓL(1,𝔽8)
hypocenterC3×C7C2×C3×#127
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ #127

2100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 336

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#127×AGL(1,𝔽7), C3⋊D3×ΓL(1,𝔽8)×#127, D3×ΓL(1,𝔽8)×#453, …
maximal normal subgroup ofD3×#127×AGL(1,𝔽7), D3×ΓL(1,𝔽8)×#453, D3×#89849⋊C3
maximal quotient ofC3⋊D3×ΓL(1,𝔽8)×#127

GAP

Past the SmallGroups library coverage — no SmallGroups id.