Finite Group Databasebeta

#553×#595 #17979031

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

Aliases

direct product#553×#595

Splittings

FittingC17×#553 ⋊ C4
SylowC17 ⋊ C4×#553

Subgroups

subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingC17×#553C4
prime radicalD17×#553C2
cosocleC22×D17C25
hypercenter#553#595
hypocenterC17C4×#553
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #553

2600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114275);