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C3×Dic3×AGL(1,ℤ/8) #11860271

order1152
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×Dic3×AGL(1,ℤ/8)

Splittings

SylowC32 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
Fitting, prime radicalC2×C32×AGL(1,ℤ/8)C2
socleC22×C32C22×D4
cosocleC2×C3×C4C24×C3
hypercenterC2×C3×AGL(1,ℤ/8)D3
hypocenterC3C3×C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×AGL(1,ℤ/8)

1245 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 94282);