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D3×#6503⋊C3 #72244255

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

Aliases

direct productD3×#6503⋊C3

Splittings

FittingC2×C3×C7×D4 ⋊ C22×C3
HallC3×ΓL(1,𝔽8) ⋊ C2×#127
SylowC7 ⋊ C3×D3×#127

Subgroups

subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽7)
commutator, socle, cosocleC22×C3×C7C24×C3
FittingC2×C3×C7×D4C22×C3
hypercenterC2×D4D3×AGL(1,𝔽7)
hypocenterC3×C7C2×C3×#127
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C2×D4

2100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 336

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#127×AGL(1,𝔽7), C3⋊D3×#6503⋊C3, D3×#90013⋊C3, …
maximal normal subgroup ofD3×#127×AGL(1,𝔽7), D3×#90013⋊C3, D3×#89970⋊C3, …
maximal quotient ofC3⋊D3×#6503⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id.