Finite Group Databasebeta

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C2×#72222036 #72246530

order6048
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productC2×#72222036

Splittings

FittingC23×C32×C7 ⋊ C22×C3
HallC32×ΓL(1,𝔽8) ⋊ C22×D4
SylowC7 ⋊ C2×C3×#3811

Subgroups

subgroupG/H
centerC22C2×D3×C3⋊AGL(1,𝔽7)
commutator, cosocleC2×C32×C7C24×C3
FrattiniC2C22×D3×C3⋊AGL(1,𝔽7)
FittingC23×C32×C7C22×C3
socleC22×C32×C7C23×C3
hypercenterC23D3×C3⋊AGL(1,𝔽7)
hypocenterC32×C7C22×C3×D4
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C22 ◁ C23

2436 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽7)×#3811
maximal normal subgroup ofC2×AGL(1,𝔽7)×#3811

GAP

Past the SmallGroups library coverage — no SmallGroups id.