Finite Group Databasebeta

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C3×#6548⋊C3 #72244391

order2016
automorphism?
homologyAbelianization (H1) = C24×C32 · Schur multiplier (H2) = C25×C3

Aliases

direct productC3×#6548⋊C3

Splittings

FittingC2×C3×C7×D4 ⋊ C2×C3
Hall#6548 ⋊ C32
HallC3×ΓL(1,𝔽8) ⋊ H(5,𝔽2)
SylowC7 ⋊ C32×H(5,𝔽2)

Subgroups

subgroupG/H
centerC2×C3C23×AGL(1,𝔽7)
commutator, cosocleC2×C7C24×C32
FrattiniC2C23×C3×AGL(1,𝔽7)
FittingC2×C3×C7×D4C2×C3
socleC2×C3×C7C24×C3
hypercenterC2×C3×D4AGL(1,𝔽7)
hypocenterC7C32×H(5,𝔽2)
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C3 ◁ C2×C3×D4

996 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

183 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×H(5,𝔽2)×AGL(1,𝔽7), D3×#6548⋊C3, #72244435, …
maximal normal subgroup ofC3×H(5,𝔽2)×AGL(1,𝔽7), D3×#6548⋊C3, #72244435, …
maximal quotient ofΓL(1,𝔽8)×#6548⋊C3, #72246213, C3×#72244406, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.