Finite Group Databasebeta

#541×#595 #17978962

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

Aliases

direct product#541×#595

Splittings

FittingC17×#541 ⋊ C4
SylowC17 ⋊ C4×#541

Subgroups

subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingC17×#541C4
prime radicalC23×D17C24
cosocleC22×D17C25
hypercenter#541#595
hypocenterC17C4×#541
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #541

2070 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, 1114206);