Finite Group Databasebeta

C22×#11763077 #17901703

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11763077

Splittings

FittingC22×C17×AGL(1,ℤ/8) ⋊ C2
SylowC17 ⋊ C22×#472

Subgroups

subgroupG/H
centerC23#10587625
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC22×C17×AGL(1,ℤ/8)C2
socleC23×C17#121
hypercenterC22×AGL(1,ℤ/8)D17
hypocenterC17C22×#472
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

2886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1036947);