Finite Group Databasebeta

C2×#14539459 #17904199

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14539459

Splittings

FittingC2×C17×#487 ⋊ C2
SylowC17 ⋊ C2×#3178

Subgroups

subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#487C2
socleC23×C17C22×D4
prime radicalC2×#10587581C22
hypercenterC2×#487D17
hypocenterC17C2×#3178
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

1906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1039443);