Finite Group Databasebeta

← Prev (#14286298) Next (#14286300) →

C3×SD16⋊#170 #14286299

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C22

Aliases

direct productC3×SD16⋊#170
unambiguous semidirect productSD16⋊(C3×#170)

Splittings

HallC3×C5 ⋊ SD16⋊C8
SylowC5 ⋊ C3×SD16⋊C8

Subgroups

subgroupG/H
centerC22×C3D4×AGL(1,𝔽5)
commutatorC4×C5C22×C3×C8
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×SD16C4
socleC22×C3×C5C4×D4
prime radicalC2×C3×C5×D4C2×C4
cosocleC4×Dic5C23×C3
hypercenterC2×C3×SD16AGL(1,𝔽5)
hypocenterC5C3×SD16⋊C8
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×SD16

352 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 11997);