Finite Group Databasebeta

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C2×C4×D3×AGL(1,𝔽5) #11756829

order960
isoclinismisoclinic class of D3×AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×D3×AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C42×D3)
unambiguous semidirect product(D3×D5)⋊C42

Splittings

FittingC2×C3×C4×C5 ⋊ C2×C4
derived, HallC3×C5 ⋊ C22×C42
SylowC5 ⋊ C2×C42×D3
SylowC3 ⋊ C22×C4×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC2×C4D3×AGL(1,𝔽5)
commutator, hypocenterC3×C5C22×C42
FrattiniC2C22×D3×AGL(1,𝔽5)
FittingC2×C3×C4×C5C2×C4
socleC22×C3×C5C22×C4
prime radicalC22×D3×D5C22
cosocleC2×C3×D5C24
LCSG ▷ C3×C5
UCSC1 ◁ C2×C4

996 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×(C2×AGL(1,𝔽5))⋊C8, #14294323, D3×#64875, …
maximal normal subgroup ofD3×(C2×AGL(1,𝔽5))⋊C8, #14294323, D3×#64875, …
maximal quotient ofC42×D3×AGL(1,𝔽5), C2×C4×Dic3×AGL(1,𝔽5), C2×D3×(C2×AGL(1,𝔽5))⋊C4, …
automorphism group ofC3⋊#672, C5×Dic15, C2×C5×D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 11024);