Finite Group Databasebeta

← Prev (#14327260) Next (#14327262) →

Q8×Dic3⋊AGL(1,𝔽5) #14327261

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productQ8×Dic3⋊AGL(1,𝔽5)

Splittings

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

Subgroups

subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×Q8C2×C4
prime radical, cosocleC22×C3×D5C24
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5Q8×C4⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×Q8

1136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 52959);