Finite Group Databasebeta

C2×#14545648 #17980048

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14545648

Splittings

SylowC17 ⋊ C2×#2975

Subgroups

subgroupG/H
centerC23C23×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC22×C22⋊C4×C17C4
socleC23×C17C23×C4
prime radicalC23×C22⋊D17C4
cosocleC2×Dic17C25
hypercenterC22×C22⋊C4#595
hypocenterC17C2×#2975
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C22⋊C4

2586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 1115292);