Finite Group Databasebeta

C2×#14543848 #17960520

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14543848

Splittings

SylowC17 ⋊ C2×#1383

Subgroups

subgroupG/H
centerC22#11763682
commutatorC8×C17C2×C42
FrattiniC2×C8C22×#595
FittingC2×C17×#106C4
socleC22×C17#340
prime radicalC23×D17SD16
cosocleC2×C8×D17C23
hypercenterC2×#106#595
hypocenterC17C2×#1383
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#106

614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1095764);