Finite Group Databasebeta

#332×#595 #17952116

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct product#332×#595

Splittings

FittingC17×#332 ⋊ C4
SylowC17 ⋊ C4×#332

Subgroups

subgroupG/H
centerC22C22⋊C4×#595
commutatorC2×C4×C17C2×C42
FrattiniC42C22×#595
FittingC17×#332C4
socleC22×C17C4×C22⋊C4
prime radicalC22×D17C2×C22⋊C4
cosocleC42×D17C23
hypercenter#332#595
hypocenterC17C4×#332
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #332

540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1087360);