Finite Group Databasebeta

C2×#14530306 #17064082

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14530306

Splittings

FittingC22×C17×#106 ⋊ C2
SylowC17 ⋊ C2×#2092

Subgroups

subgroupG/H
centerC24D4×D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC22×C17×#106C2
socleC24×C17C2×D4
prime radicalC23×D68C22
hypercenterC22×#106D17
hypocenterC17C2×#2092
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#106

1366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 199326);