Finite Group Databasebeta

#392×#595 #17963108

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct product#392×#595

Splittings

FittingC17×#392 ⋊ C4
SylowC17 ⋊ C4×#392

Subgroups

subgroupG/H
center, FrattiniC23C23×#595
commutator, socleC23×C17C23×C4
FittingC17×#392C4
prime radicalD17×#392C2
cosocleC23×D17C24
hypercenter#392#595
hypocenterC17C4×#392
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #392

3502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1098352);