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Dic3×Dic7⋊C4 #13053879

order1344
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productDic3×Dic7⋊C4

Splittings

HallC3×C7 ⋊ C4×C4⋊C4
SylowC7 ⋊ Dic3×C4⋊C4
SylowC3 ⋊ C4×Dic7⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C2×D3×D7
commutatorC2×C3×C7C2×C42
FittingC22×C3×C4×C7C22
socle, prime radical, cosocleC23×C3×C7C23
hypercenterC22×C4D3×D7
hypocenterC3×C7C4×C4⋊C4
LCSG ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C23 ◁ C22×C4

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1344

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 3168);