Finite Group Databasebeta

#585×#595 #17981042

order4352
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct product#585×#595

Splittings

FittingC17×#585 ⋊ C4
SylowC17 ⋊ C4×#585

Subgroups

subgroupG/H
centerC4C24×#595
commutator, socleC2×C17C25×C4
FrattiniC2C25×#595
FittingC17×#585C4
prime radicalD17×#585C2
cosocleC2×D17C26
hypercenter#585#595
hypocenterC17C4×#585
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ #585

11346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

Conjugacy classes & character table

272 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1116286);