Finite Group Databasebeta

C2×#14544477 #17968201

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productC2×#14544477

Splittings

SylowC17 ⋊ C2×#1738

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC4×C17C22×C42
FrattiniC2×C4C23×#595
FittingC22×M16×C17C4
socleC22×C17C2×#95
prime radicalC24×D17Q8
cosocleC2×C4×D17C24
hypercenterC22×M16#595
hypocenterC17C2×#1738
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

2110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1103445);