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C2×AGL(1,ℤ/8)×Dic17 #17898388

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×AGL(1,ℤ/8)×Dic17

Splittings

SylowC17 ⋊ C2×C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC23C2×D4×D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
Fitting, prime radicalC22×C17×AGL(1,ℤ/8)C2
socleC23×C17C22×D4
cosocleC2×C4×C17C25
hypercenterC22×AGL(1,ℤ/8)D17
hypocenterC17C2×C4×AGL(1,ℤ/8)
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

3242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033632);