Finite Group Databasebeta

← Prev (#14319619) Next (#14319621) →

C4×Q8×ΓL(1,𝔽16) #14319620

order1920
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×Q8×ΓL(1,𝔽16)

Splittings

FittingC3×C4×C5×Q8 ⋊ C4
HallC3×C5 ⋊ C42×Q8
SylowC5 ⋊ C4×Q8×Dic3
SylowC3 ⋊ C4×Q8×AGL(1,𝔽5)

Subgroups

subgroupG/H
centerC2×C4C22×ΓL(1,𝔽16)
commutatorC2×C3×C5C22×C42
FrattiniC22C23×ΓL(1,𝔽16)
FittingC3×C4×C5×Q8C4
socleC22×C3×C5C23×C4
prime radical, cosocleC22×C3×D5C24
hypercenterC4×Q8ΓL(1,𝔽16)
hypocenterC3×C5C42×Q8
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C4×Q8

1368 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45318);