Finite Group Databasebeta

#432×#595 #17968651

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct product#432×#595

Splittings

FittingC17×#432 ⋊ C4
SylowC17 ⋊ C4×#432

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×#595
commutator, socleC22×C17C22×C42
FittingC17×#432C4
prime radicalC23×D17C22×C4
cosocleC2×C4×D17C24
hypercenter#432#595
hypocenterC17C4×#432
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #432

1206 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, 1103895);