Finite Group Databasebeta

D17×#3401 #17915322

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productD17×#3401

Splittings

FittingC17×#3401 ⋊ C2
SylowC17 ⋊ C2×#3401

Subgroups

subgroupG/H
centerC22C22×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC17×#3401C2
socleC22×C17C23×D4
prime radicalD17×#496C2
hypercenter#3401D17
hypocenterC17C2×#3401
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3401

2002 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

290 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1050566);