Finite Group Databasebeta

D17×#2947 #17898425

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productD17×#2947

Splittings

FittingC17×#2947 ⋊ C2
SylowC17 ⋊ C2×#2947

Subgroups

subgroupG/H
centerC22C22×D4×D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC17×#2947C2
socleC22×C17C23×D4
prime radicalC2×#41×D17C22
cosocleC2×C4×C17C25
hypercenter#2947D17
hypocenterC17C2×#2947
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ #117 ◁ #2947

2730 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033669);