Finite Group Databasebeta

#510×#595 #17978601

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

Aliases

direct product#510×#595

Splittings

FittingC17×#510 ⋊ C4
SylowC17 ⋊ C4×#510

Subgroups

subgroupG/H
centerC2C2×D8×#595
commutatorC8×C17C23×C4
FrattiniC8C23×#595
FittingC17×#510C4
socleC2×C17C2×C4×D8
prime radical#135×D17C22
cosocleC8×D17C24
hypercenter#510#595
hypocenterC17C4×#510
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1113845);