Finite Group Databasebeta

← Prev (#72277214) Next (#72277216) →

D3×AGL(1,𝔽5)×#97 #72277215

order3840
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C24×C42

Aliases

direct productD3×AGL(1,𝔽5)×#97

Splittings

FittingC3×C5×#97 ⋊ C2×C4
HallC3×C5 ⋊ C2×C4×#97
SylowC5 ⋊ C4×D3×#97
SylowC3 ⋊ C2×AGL(1,𝔽5)×#97

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C2×C43
FittingC3×C5×#97C2×C4
socleC22×C3×C5C22×C42
prime radicalC22×D3×D5C22×C4
cosocleC2×C3×C4×D5C24
hypercenter#97D3×AGL(1,𝔽5)
hypocenterC3×C5C2×C4×#97
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ #97

3580 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.