Finite Group Databasebeta

SD16×#13050573 #35375837

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productSD16×#13050573

Splittings

FittingC8×SD16×C83 ⋊ C2
SylowC83 ⋊ M16×SD16

Subgroups

subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC8×SD16×C83C2
socleC22×C83C2×C4×D4
prime radicalC2×D4×D83C2×C4
cosocleC42×C83C24
hypercenterC8×SD16D83
hypocenterC83M16×SD16
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×SD16

716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

2366 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 141001);