Finite Group Databasebeta

SD16×#63218 #17005757

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

Aliases

direct productSD16×#63218

Splittings

FittingC8×SD16×C17 ⋊ C2
SylowC17 ⋊ M16×SD16

Subgroups

subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC8×SD16×C17C2
socleC22×C17C2×C4×D4
prime radicalC2×D4×D17C2×C4
cosocleC42×C17C24
hypercenterC8×SD16D17
hypocenterC17M16×SD16
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×SD16

716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 141001);