Finite Group Databasebeta

C2×#14530627 #17187559

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14530627

Splittings

FittingC2×C17×#346 ⋊ C2
SylowC17 ⋊ C2×#2171

Subgroups

subgroupG/H
centerC2×C8C2×D68
commutatorC4×C17C23×C8
FrattiniC2×C8C23×D17
FittingC2×C17×#346C2
socleC22×C17C8×D4
prime radicalC2×#10587590C4
cosocleC2×C8×C17C24
hypercenterC2×#346D17
hypocenterC17C2×#2171
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C22×C16 ◁ C2×#346

654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 322803);