Finite Group Databasebeta

#384×#595 #17962961

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42

Aliases

direct product#384×#595

Splittings

FittingC17×#384 ⋊ C4
SylowC17 ⋊ C4×#384

Subgroups

subgroupG/H
center, FrattiniC23C23×#595
commutatorC22×C17C22×C42
FittingC17×#384C4
socleC23×C17C23×C4
prime radical, cosocleC23×D17C24
hypercenter#384#595
hypocenterC17C4×#384
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #384

2094 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 1098205);