Finite Group Databasebeta

C2×#14545036 #17978215

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14545036

Splittings

FittingC2×C17×#120 ⋊ C4
SylowC17 ⋊ C2×#2120

Subgroups

subgroupG/H
centerC22D17⋊#99
commutatorC23×C17C23×C4
FrattiniC23C23×#595
FittingC2×C17×#120C4
socleC22×C17C2×#99
prime radicalC2×#11763315C2
cosocleC2×C22⋊D17C24
hypercenterC2×#120#595
hypocenterC17C2×#2120
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#120

1398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1113459);