Finite Group Databasebeta

#349×#595 #17960708

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct product#349×#595

Splittings

FittingC17×#349 ⋊ C4
SylowC17 ⋊ C4×#349

Subgroups

subgroupG/H
centerC4C22⋊C4×#595
commutatorC22×C17C2×C4×C8
FrattiniC2×C8C22×#595
FittingC17×#349C4
socleC2×C17C4×C22⋊C8
prime radicalC23×D17C2×C8
cosocleC2×C8×D17C23
hypercenter#349#595
hypocenterC17C4×#349
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C8 ◁ #349

522 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, 1095952);