Finite Group Databasebeta

#519×#595 #17978869

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct product#519×#595

Splittings

FittingC17×#519 ⋊ C4
SylowC17 ⋊ C4×#519

Subgroups

subgroupG/H
center, FrattiniC22C24×#595
commutatorC2×C17C23×C42
FittingC17×#519C4
socleC22×C17C24×C4
prime radicalC23×D17C24
cosocleC22×D17C25
hypercenter#519#595
hypocenterC17C4×#519
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ #519

3402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

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, 1114113);