Finite Group Databasebeta

C2×#14545519 #17979689

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#14545519

Splittings

SylowC17 ⋊ C2×#2933

Subgroups

subgroupG/H
centerC23C23×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC2×C17×C22⋊Q8C4
socleC23×C17C23×C4
prime radicalC2×#11763322C2
cosocleC2×Dic17C25
hypercenterC2×C22⋊Q8#595
hypocenterC17C2×#2933
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

2926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

212 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114933);