Finite Group Databasebeta

C2×#14544587 #17968572

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#14544587

Splittings

FittingC2×C17×#106 ⋊ C4
SylowC17 ⋊ C2×#1772

Subgroups

subgroupG/H
centerC23D4×#595
commutatorC4×C17C22×C42
FrattiniC2×C4C23×#595
FittingC2×C17×#106C4
socleC23×C17C4×D4
prime radicalC23×D17#41
cosocleC2×C4×D17C24
hypercenterC2×#106#595
hypocenterC17C2×#1772
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

1102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1103816);