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AGL(1,ℤ/8)×#3633 #17982867

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×#3633

Splittings

FittingC17×AGL(1,ℤ/8) ⋊ C8
SylowC17 ⋊ C8×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2C2×D4×#3633
commutatorC4×C17C23×C8
FrattiniC4C23×#3633
FittingC17×AGL(1,ℤ/8)C8
socleC2×C17C2×C8×D4
prime radicalAGL(1,ℤ/8)×D17C4
cosocleC4×#595C24
hypercenterAGL(1,ℤ/8)#3633
hypocenterC17C8×AGL(1,ℤ/8)
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 136

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/8)×AGL(1,𝔽17), #453×#3633, #72242854
maximal normal subgroup ofAGL(1,ℤ/8)×AGL(1,𝔽17), #453×#3633, #72242854

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1118111);