Finite Group Databasebeta

SD16×#11929607 #34259702

order20224
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productSD16×#11929607

Splittings

FittingC8×SD16×C79 ⋊ C2
SylowC79 ⋊ M16×SD16

Subgroups

subgroupG/H
centerC2×C4C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC42C23×D79
FittingC8×SD16×C79C2
socleC22×C79C2×C4×D4
prime radicalC2×D4×D79C2×C4
cosocleC42×C79C24
hypercenterC8×SD16D79
hypocenterC79M16×SD16
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×SD16

716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5056

Conjugacy classes & character table

2254 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 141001);