Finite Group Databasebeta

C2×#14545446 #17979565

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

Aliases

direct productC2×#14545446

Splittings

SylowC17 ⋊ C2×#2916

Subgroups

subgroupG/H
centerC22C22×C4⋊#595
commutatorC4×C17C24×C4
FrattiniC4C24×#595
FittingC2×C17×#131C4
socleC22×C17C22×C4⋊C4
prime radicalC2×#41×D17C22
cosocleC4×D17C25
hypercenterC2×#131#595
hypocenterC17C2×#2916
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131

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, 1114809);