Finite Group Databasebeta

#431×#595 #17968632

order4352
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct product#431×#595

Splittings

FittingC17×#431 ⋊ C4
SylowC17 ⋊ C4×#431

Subgroups

subgroupG/H
centerC42C22×#595
commutatorC2×C17C22×C4×C8
FrattiniC2×C4C23×#595
FittingC17×#431C4
socleC22×C17C22×C42
prime radicalC23×D17C22×C4
cosocleC2×C4×D17C24
hypercenter#431#595
hypocenterC17C4×#431
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C42 ◁ #431

1318 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, 1103876);