Finite Group Databasebeta

#449×#595 #17971178

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#449×#595

Splittings

FittingC17×#449 ⋊ C4
SylowC17 ⋊ C4×#449

Subgroups

subgroupG/H
centerC22C2×D4×#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC17×#449C4
socleC22×C17C2×C4×D4
prime radicalD17×#449C2
cosocleC2×C4×D17C24
hypercenter#449#595
hypocenterC17C4×#449
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

1564 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

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, 1106422);