Finite Group Databasebeta

C2×#14530959 #17189059

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14530959

Splittings

FittingC2×C17×#365 ⋊ C2
SylowC17 ⋊ C2×#2231

Subgroups

subgroupG/H
centerC22#11763098
commutator, cosocleC2×C8×C17C24
FrattiniC2×C8C23×D17
FittingC2×C17×#365C2
socleC22×C17#476
prime radicalC2×#10587590C22
hypercenterC2×#365D17
hypocenterC17C2×#2231
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 324303);