Finite Group Databasebeta

SD16×#4318 #14725214

order2816
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productSD16×#4318

Splittings

SylowC11 ⋊ M16×SD16

Subgroups

subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C4×C11×SD16C2
socleC22×C11C2×C4×D4
prime radicalC22×D4×C11C2×C4
cosocleC42×C11C24
hypercenterC2×C4×SD16D11
hypocenterC11M16×SD16
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×SD16

716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 141009);