Finite Group Databasebeta

D17×#2212 #17188692

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD17×#2212

Splittings

FittingC17×#2212 ⋊ C2
SylowC17 ⋊ C2×#2212

Subgroups

subgroupG/H
centerC2D17×#459
commutator, cosocleC2×C8×C17C24
FrattiniC2×C8C23×D17
FittingC17×#2212C2
socleC2×C17C2×#459
prime radicalD17×#509C2
hypercenter#2212D17
hypocenterC17C2×#2212
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2212

706 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 323936);