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AGL(1,ℤ/8)×#3624 #17966614

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

Aliases

direct productAGL(1,ℤ/8)×#3624

Splittings

SylowC17 ⋊ C8×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C2×D4×#595
commutatorC4×C17C23×C8
FrattiniC2×C4C23×#595
Fitting, prime radicalC2×C17×AGL(1,ℤ/8)C4
socleC22×C17C2×C4×D4
cosocleC4×Dic17C24
hypercenterC2×AGL(1,ℤ/8)#595
hypocenterC17C8×AGL(1,ℤ/8)
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1101858);