Finite Group Databasebeta

C2×D17×#350 #17187019

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×D17×#350

Splittings

FittingC2×C17×#350 ⋊ C2
SylowC17 ⋊ C22×#350

Subgroups

subgroupG/H
centerC2×C8D4×D17
commutatorC4×C17C23×C8
FrattiniC2×C8C23×D17
FittingC2×C17×#350C2
socleC22×C17C2×C22⋊C8
prime radicalC2×#41×D17C4
cosocleC2×C8×C17C24
hypercenterC2×#350D17
hypocenterC17C22×#350
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#350

1174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 322263);