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C2×D32×AGL(1,ℤ/8) #72243173

order2304
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC2×D32×AGL(1,ℤ/8)

Splittings

FittingC2×C32×AGL(1,ℤ/8) ⋊ C22
SylowC32 ⋊ C23×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C2×D32×D4
commutator, cosocleC32×C4C26
FrattiniC4C24×D32
FittingC2×C32×AGL(1,ℤ/8)C22
socleC22×C32C23×D4
hypercenterC2×AGL(1,ℤ/8)D32
hypocenterC32C23×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

27480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD32×#3151
maximal normal subgroup ofD32×#3151
maximal quotient ofD32×#3151

GAP

Past the SmallGroups library coverage — no SmallGroups id.