Finite Group Databasebeta

#529×#595 #17978902

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct product#529×#595

Splittings

FittingC17×#529 ⋊ C4
SylowC17 ⋊ C4×#529

Subgroups

subgroupG/H
centerC2×C4C23×#595
commutator, socleC22×C17C24×C4
FrattiniC22C24×#595
FittingC17×#529C4
prime radical#121×D17C22
cosocleC22×D17C25
hypercenter#529#595
hypocenterC17C4×#529
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #529

2670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

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, 1114146);