Finite Group Databasebeta

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C2×#72222121 #72246548

order14112
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productC2×#72222121

Splittings

FittingC23×C3×C72 ⋊ C22×C3
HallC3×#3861 ⋊ C22×D4
SylowC72 ⋊ C22×C3×#67

Subgroups

subgroupG/H
centerC22C2×#13183634
commutator, cosocleC2×C3×C72C24×C3
FrattiniC2C22×#13183634
FittingC23×C3×C72C22×C3
socleC22×C3×C72C23×C3
hypercenterC23#13183634
hypocenterC3×C72C22×C3×D4
LCSG ▷ C2×C3×C72 ▷ C3×C72
UCSC1 ◁ C22 ◁ C23

3362 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D3×#72210376
maximal normal subgroup ofC2×D3×#72210376

GAP

Past the SmallGroups library coverage — no SmallGroups id.