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D32×AGL(1,ℤ/8) #11918652

order1152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productD32×AGL(1,ℤ/8)

Splittings

FittingC32×AGL(1,ℤ/8) ⋊ C22
SylowC32 ⋊ C22×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2C2×D32×D4
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC32×AGL(1,ℤ/8)C22
socleC2×C32C23×D4
hypercenterAGL(1,ℤ/8)D32
hypocenterC32C22×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

3589 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

99 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72213893, D3×#10595100, AGL(1,ℤ/8)×GO+(4,𝔽2), …
maximal normal subgroup of#72213893, AGL(1,ℤ/8)×GO+(4,𝔽2), D32×#453, …
maximal quotient of#72219800, D3×#10595100, AGL(1,ℤ/8)×((C3⋊D3)⋊C3)⋊C2, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 152663);