Finite Group Databasebeta

D17×#3042 #17901213

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productD17×#3042

Splittings

FittingC17×#3042 ⋊ C2
SylowC17 ⋊ C2×#3042

Subgroups

subgroupG/H
centerC22C22×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC17×#3042C2
socleC22×C17C23×D4
prime radicalC2×AGL(1,ℤ/8)×D17C2
hypercenter#3042D17
hypocenterC17C2×#3042
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ #117 ◁ #3042

2882 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, 1036457);