Finite Group Databasebeta

D17×#2162 #17187385

order4352
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C24×C4

Aliases

direct productD17×#2162

Splittings

FittingC17×#2162 ⋊ C2
SylowC17 ⋊ C2×#2162

Subgroups

subgroupG/H
centerC4×C8C22×D17
commutatorC2×C17C23×C16
FrattiniC2×C8C23×D17
FittingC17×#2162C2
socleC22×C17C23×C8
prime radicalC23×D17C2×C8
cosocleC2×C8×C17C24
hypercenter#2162D17
hypocenterC17C2×#2162
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C4×C8 ◁ #2162

726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 322629);