Finite Group Databasebeta

SD16×D137 #17984100

order4384
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productSD16×D137

Splittings

FittingSD16×C137 ⋊ C2
SylowC137 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC2D4×D137
commutator, cosocleC4×C137C23
FrattiniC4C22×D137
FittingSD16×C137C2
socleC2×C137C2×D4
prime radicalD4×D137C2
hypercenterSD16D137
hypocenterC137C2×SD16
LCSG ▷ C4×C137 ▷ C2×C137 ▷ C137
UCSC1 ◁ C2 ◁ C4 ◁ SD16

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1096

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4384, 158);