Finite Group Databasebeta

C2×#14539651 #17904994

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

Aliases

direct productC2×#14539651

Splittings

FittingC2×C17×#536 ⋊ C2
SylowC17 ⋊ C2×#3200

Subgroups

subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#536C2
socleC23×C17C22×D4
prime radicalC2×#11763373C2
hypercenterC2×#536D17
hypocenterC17C2×#3200
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#536

2314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1040238);