Finite Group Databasebeta

#346×#595 #17960417

order4352
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C2×C42

Aliases

direct product#346×#595

Splittings

FittingC17×#346 ⋊ C4
SylowC17 ⋊ C4×#346

Subgroups

subgroupG/H
center, FrattiniC2×C8C22×#595
commutatorC2×C17C42×C8
FittingC17×#346C4
socleC22×C17C2×C4×C8
prime radicalC22×D17C22×C8
cosocleC2×C8×D17C23
hypercenter#346#595
hypocenterC17C4×#346
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ #346

510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1095661);