Finite Group Databasebeta

C2×#14528760 #17033666

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14528760

Splittings

FittingC2×C17×#413 ⋊ C2
SylowC17 ⋊ C2×#1796

Subgroups

subgroupG/H
centerC22#11762664
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#413C2
socleC22×C17#379
prime radicalC22×#10587697C2
cosocleC22×C4×C17C24
hypercenterC2×#413D17
hypocenterC17C2×#1796
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#413

3602 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 168910);