Finite Group Databasebeta

← Prev (#14295154) Next (#14295156) →

C8×#6763 #14295155

order1920
isoclinismisoclinic class of #6758
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC8×#6763

Splittings

FittingC22×C3×C5×C8 ⋊ C4
HallC3×C5 ⋊ C8×C22⋊C4
SylowC5 ⋊ C8×#217
SylowC3 ⋊ C8×C22⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
centerC2×C8C2×ΓL(1,𝔽16)
commutatorC2×C3×C5C2×C4×C8
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC22×C3×C5×C8C4
socleC22×C3×C5C2×C42
prime radicalC23×C3×D5C2×C4
cosocleC2×C3×C4×D5C23
hypercenterC22×C8ΓL(1,𝔽16)
hypocenterC3×C5C8×C22⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C8 ◁ C22×C8

768 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20853);