Finite Group Databasebeta

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C2×#67×#64424 #72246366

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

Aliases

direct productC2×#67×#64424

Splittings

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

Subgroups

subgroupG/H
centerC22C2×D3×#64424
commutator, cosocleC2×C3×C72C24×C3
FrattiniC2C22×D3×#64424
FittingC23×C3×C72C22×C3
socleC22×C3×C72C23×C3
hypercenterC23D3×#64424
hypocenterC3×C72C22×C3×D4
LCSG ▷ C2×C3×C72 ▷ C3×C72
UCSC1 ◁ C22 ◁ C23

5390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1176

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D3×D4×#64424
maximal normal subgroup ofC2×D3×D4×#64424

GAP

Past the SmallGroups library coverage — no SmallGroups id.