Finite Group Databasebeta

#334×#595 #17952316

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

Aliases

direct product#334×#595

Splittings

FittingC17×#334 ⋊ C4
SylowC17 ⋊ C4×#334

Subgroups

subgroupG/H
centerC2×C4D4×#595
commutatorC4×C17C2×C4×C8
FrattiniC42C22×#595
FittingC17×#334C4
socleC22×C17C4×C4⋊C4
prime radicalC22×D17C2×C4⋊C4
cosocleC42×D17C23
hypercenter#334#595
hypocenterC17C4×#334
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C42 ◁ #334

470 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, 1087560);