Finite Group Databasebeta

#508×#595 #17978595

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#508×#595

Splittings

FittingC17×#508 ⋊ C4
SylowC17 ⋊ C4×#508

Subgroups

subgroupG/H
centerC4D8×#595
commutatorC8×C17C23×C4
FrattiniC8C23×#595
FittingC17×#508C4
socleC2×C17C2×C4×D8
prime radicalD17×#508C2
cosocleC8×D17C24
hypercenter#508#595
hypocenterC17C4×#508
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #508

690 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, 1113839);