Finite Group Databasebeta

C2×#14545670 #17980075

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

Aliases

direct productC2×#14545670

Splittings

SylowC17 ⋊ C2×#2980

Subgroups

subgroupG/H
centerC23C23×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC2×C17×#124C4
socleC23×C17C23×C4
prime radicalC2×#11763358C2
cosocleC2×Dic17C25
hypercenterC2×#124#595
hypocenterC17C2×#2980
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#124

2186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

188 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1115319);