Finite Group Databasebeta

#504×#595 #17978138

order4352
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct product#504×#595

Splittings

FittingC17×#504 ⋊ C4
SylowC17 ⋊ C4×#504

Subgroups

subgroupG/H
centerC16C22×#595
commutator, socleC2×C17C22×C4×C8
FrattiniC8C23×#595
FittingC17×#504C4
prime radical#41×D17C2×C4
cosocleC8×D17C24
hypercenter#504#595
hypocenterC17C4×#504
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C16 ◁ #504

834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

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, 1113382);