Finite Group Databasebeta

#340×#595 #17956614

order4352
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C23×C42

Aliases

direct product#340×#595

Splittings

FittingC17×#340 ⋊ C4
SylowC17 ⋊ C4×#340

Subgroups

subgroupG/H
centerC23D4×#595
commutatorC4×C17C43
FrattiniC22×C4C22×#595
FittingC17×#340C4
socleC23×C17C4×D4
prime radicalC23×D17C2×D4
cosocleC22×C4×D17C23
hypercenter#340#595
hypocenterC17C4×#340
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

1182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 1091858);