Finite Group Databasebeta

← Prev (#14479000) Next (#14479002) →

D3×#66258 #14479001

order1920
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productD3×#66258

Splittings

FittingC2×C3×C5×D4 ⋊ C2×C4
HallC3×C5 ⋊ C2×#518
SylowC5 ⋊ D3×#518
SylowC3 ⋊ C2×#66258

Subgroups

subgroupG/H
center, FrattiniC2C23×D3×AGL(1,𝔽5)
commutator, socleC2×C3×C5C24×C4
FittingC2×C3×C5×D4C2×C4
prime radicalC2×D3×D4×D5C2
cosocleC2×C3×D5C25
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#518
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×D4

3840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×H(5,𝔽2), D3×#10604461, D3×#10603919, …
maximal normal subgroup ofD3×AGL(1,𝔽5)×H(5,𝔽2), D3×#10604461, D3×#10603919, …
maximal quotient of#72260182, #72260215, #72260246

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 204699);