Finite Group Databasebeta

← Prev (#72259583) Next (#72259585) →

D3×AGL(1,𝔽5)×#453 #72259584

order7680
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productD3×AGL(1,𝔽5)×#453

Splittings

FittingC3×C5×#453 ⋊ C2×C4
HallC3×C5 ⋊ C2×C4×#453
SylowC5 ⋊ C4×D3×#453
SylowC3 ⋊ C2×AGL(1,𝔽5)×#453

Subgroups

subgroupG/H
centerC2D3×AGL(1,𝔽5)×#120
commutatorC2×C3×C4×C5C24×C4
FrattiniC2×C4C23×D3×AGL(1,𝔽5)
FittingC3×C5×#453C2×C4
socleC2×C3×C5C2×C4×#120
prime radicalD3×D5×#453C2
cosocleC2×C3×C4×D5C25
hypercenter#453D3×AGL(1,𝔽5)
hypocenterC3×C5C2×C4×#453
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

21600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×#5935
holomorph ofC3×C5×D4

GAP

Past the SmallGroups library coverage — no SmallGroups id.