Finite Group Databasebeta

C2×#14533943 #17204702

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C27×C4

Aliases

direct productC2×#14533943

Splittings

FittingC22×C17×C22⋊Q8 ⋊ C2
SylowC17 ⋊ C2×#2561

Subgroups

subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC22×C17×C22⋊Q8C2
socleC24×C17C24
prime radicalC25×D17C22
hypercenterC22×C22⋊Q8D17
hypocenterC17C2×#2561
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

4166 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, 339946);