Finite Group Databasebeta

#560×#595 #17979218

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct product#560×#595

Splittings

FittingC17×#560 ⋊ C4
SylowC17 ⋊ C4×#560

Subgroups

subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingC17×#560C4
prime radicalD17×#560C2
cosocleC22×D17C25
hypercenter#560#595
hypocenterC17C4×#560
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #560

2568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114462);