Finite Group Databasebeta

C2×#14528898 #17034191

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14528898

Splittings

SylowC17 ⋊ C2×#1830

Subgroups

subgroupG/H
centerC22#11762672
commutatorC23×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#519C2
socleC22×C17#381
prime radicalC24×C17C22×C4
cosocleC22×C4×C17C24
hypercenterC2×#519D17
hypocenterC17C2×#1830
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#519

1218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 169435);