Finite Group Databasebeta

SD16⋊C8×D73 #33055365

order18688
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productSD16⋊C8×D73

Splittings

FittingC73×SD16⋊C8 ⋊ C2
SylowC73 ⋊ C2×SD16⋊C8

Subgroups

subgroupG/H
centerC2×C4C2×D4×D73
commutatorC4×C73C23×C8
FrattiniC42C23×D73
FittingC73×SD16⋊C8C2
socleC22×C73C2×C4×D4
prime radicalC2×D4×D73C2×C4
cosocleC42×C73C24
hypercenterSD16⋊C8D73
hypocenterC73C2×SD16⋊C8
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

1672 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 138949);