Finite Group Databasebeta

C2×#14529266 #17036191

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#14529266

Splittings

SylowC17 ⋊ C2×#1903

Subgroups

subgroupG/H
centerC22#11762689
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
Fitting, prime radicalC22×C17×AGL(1,ℤ/8)C2
socleC22×C17#386
cosocleC22×C4×C17C24
hypercenterC22×AGL(1,ℤ/8)D17
hypocenterC17C2×#1903
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

1782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 171435);