Finite Group Databasebeta

SD16×D89 #15668024

order2848
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productSD16×D89

Splittings

FittingSD16×C89 ⋊ C2
SylowC89 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC2D4×D89
commutator, cosocleC4×C89C23
FrattiniC4C22×D89
FittingSD16×C89C2
socleC2×C89C2×D4
prime radicalD4×D89C2
hypercenterSD16D89
hypocenterC89C2×SD16
LCSG ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2 ◁ C4 ◁ SD16

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 712

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2848, 158);