Finite Group Databasebeta

#341×#595 #17956620

order4352
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C22×C42

Aliases

direct product#341×#595

Splittings

FittingC17×#341 ⋊ C4
SylowC17 ⋊ C4×#341

Subgroups

subgroupG/H
centerC2×C4D4×#595
commutatorC4×C17C43
FrattiniC22×C4C22×#595
FittingC17×#341C4
socleC22×C17C4×C4⋊C4
prime radicalC23×D17C2×Q8
cosocleC22×C4×D17C23
hypercenter#341#595
hypocenterC17C4×#341
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #341

910 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1091864);