Finite Group Databasebeta

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C22×#6503⋊C3 #72230194

order2688
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×#6503⋊C3

Splittings

FittingC23×C7×D4 ⋊ C2×C3
HallC22×#6503 ⋊ C3
HallΓL(1,𝔽8) ⋊ C22×#127
SylowC7 ⋊ C22×C3×#127

Subgroups

subgroupG/H
centerC24C22×AGL(1,𝔽7)
commutator, cosocleC22×C7C25×C3
FrattiniC22C24×AGL(1,𝔽7)
FittingC23×C7×D4C2×C3
socleC24×C7C23×C3
hypercenterC23×D4AGL(1,𝔽7)
hypocenterC7C22×C3×#127
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C23×D4

6000 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.