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AGL(1,ℤ/8)×#157 #11860281

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

Aliases

direct productAGL(1,ℤ/8)×#157

Splittings

FittingC32×AGL(1,ℤ/8) ⋊ C4
SylowC32 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2C2×D4×#157
commutatorC32×C4C23×C4
FrattiniC4C23×#157
FittingC32×AGL(1,ℤ/8)C4
socleC2×C32C2×C4×D4
prime radicalC3⋊D3×AGL(1,ℤ/8)C2
cosocleC4×C3⋊D3C24
hypercenterAGL(1,ℤ/8)#157
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

846 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/8)×PSU(3,𝔽2), AGL(1,ℤ/8)×GO+(4,𝔽2), AGL(1,ℤ/8)×AGL(1,𝔽9), …
maximal normal subgroup ofAGL(1,ℤ/8)×PSU(3,𝔽2), AGL(1,ℤ/8)×GO+(4,𝔽2), AGL(1,ℤ/8)×AGL(1,𝔽9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 94292);