Finite Group Databasebeta

C2×D17×#451 #17900633

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×D17×#451

Splittings

FittingC2×C17×#451 ⋊ C2
SylowC17 ⋊ C22×#451

Subgroups

subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#451C2
socleC23×C17C22×D4
prime radicalC24×D17D4
hypercenterC2×#451D17
hypocenterC17C22×#451
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

4982 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1035877);