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C4×D3×AGL(1,ℤ/8) #11659243

order768
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×D3×AGL(1,ℤ/8)

Splittings

FittingC3×C4×AGL(1,ℤ/8) ⋊ C2
SylowC3 ⋊ C2×C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C4C2×D3×D4
commutatorC3×C4C24×C4
FrattiniC2×C4C24×D3
FittingC3×C4×AGL(1,ℤ/8)C2
socleC22×C3C23×D4
prime radicalC2×D3×AGL(1,ℤ/8)C2
cosocleC2×C3×C4C25
hypercenterC4×AGL(1,ℤ/8)D3
hypocenterC3C2×C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

3242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#60176, C4×D3×#575, #72227388, …
maximal normal subgroup ofD3×#61451, D3×#60176, C4×D3×#575, …
maximal quotient ofD3×#21452, #72227388, C4×#10595100, …
automorphism group ofC5×D24, C5×Dic12

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1033624);