Finite Group Databasebeta

C2×#14526671 #16924463

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14526671

Splittings

SylowC17 ⋊ C2×#1298

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic17
commutatorC2×C4×C17C2×C42
FrattiniC23×C4C22×D17
FittingC2×C17×#407C2
socleC23×C17#95
prime radicalC25×C17Q8
cosocleC23×C4×C17C23
hypercenterC2×#407D17
hypocenterC17C2×#1298
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×#407

938 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

524 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 59707);