Finite Group Databasebeta

#543×#595 #17978963

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

Aliases

direct product#543×#595

Splittings

FittingC17×#543 ⋊ C4
SylowC17 ⋊ C4×#543

Subgroups

subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingC17×#543C4
prime radicalC24×D17C23
cosocleC22×D17C25
hypercenter#543#595
hypocenterC17C4×#543
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #543

2602 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

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, 1114207);