Finite Group Databasebeta

C2×#14529847 #17061328

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#14529847

Splittings

FittingC2×C17×#344 ⋊ C2
SylowC17 ⋊ C2×#2009

Subgroups

subgroupG/H
centerC22#11762719
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC2×C17×#344C2
socleC22×C17#392
prime radicalC2×#11763609C2
hypercenterC2×#344D17
hypocenterC17C2×#2009
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#344

1926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 196572);