Finite Group Databasebeta

C2×#14531921 #17196899

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C26×C42

Aliases

direct productC2×#14531921

Splittings

FittingC2×C17×#390 ⋊ C2
SylowC17 ⋊ C2×#2375

Subgroups

subgroupG/H
centerC24C23×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC2×C17×#390C2
socleC24×C17C24
prime radicalC22×#10587623C2
cosocleC23×C17C25
hypercenterC2×#390D17
hypocenterC17C2×#2375
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#390

4246 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, 332143);