Finite Group Databasebeta

#327×#595 #17952046

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct product#327×#595

Splittings

FittingC17×#327 ⋊ C4
SylowC17 ⋊ C4×#327

Subgroups

subgroupG/H
centerC22C22⋊C4×#595
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC17×#327C4
socleC22×C17C4×C22⋊C4
prime radical#121×D17C22
cosocleC22×C4×D17C23
hypercenter#327#595
hypocenterC17C4×#327
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

816 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

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, 1087290);