Finite Group Databasebeta

M16×#4323 #14725193

order2816
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productM16×#4323

Splittings

FittingD4×C11×M16 ⋊ C2
SylowC11 ⋊ M16×D8

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingD4×C11×M16C2
socleC22×C11C2×C4×D4
prime radicalC22×#4323C4
cosocleC42×C11C24
hypercenterD4×M16D11
hypocenterC11M16×D8
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ D4×M16

794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 140988);