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AGL(1,ℤ/8)×C3⋊Dic3 #11860270

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

Aliases

direct productAGL(1,ℤ/8)×C3⋊Dic3

Splittings

SylowC32 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C2×D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
Fitting, prime radicalC2×C32×AGL(1,ℤ/8)C2
socleC22×C32C22×D4
cosocleC2×C32×C4C24
hypercenterC2×AGL(1,ℤ/8)C3⋊D3
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

1644 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 94281);