Finite Group Databasebeta

SD16⋊C8×D83 #35373785

order21248
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productSD16⋊C8×D83

Splittings

FittingC83×SD16⋊C8 ⋊ C2
SylowC83 ⋊ C2×SD16⋊C8

Subgroups

subgroupG/H
centerC2×C4C2×D4×D83
commutatorC4×C83C23×C8
FrattiniC42C23×D83
FittingC83×SD16⋊C8C2
socleC22×C83C2×C4×D4
prime radicalC2×D4×D83C2×C4
cosocleC42×C83C24
hypercenterSD16⋊C8D83
hypocenterC83C2×SD16⋊C8
LCSG ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

1892 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 138949);