Finite Group Databasebeta

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C2×D3×D5⋊C8 #11756814

order960
isoclinismisoclinic class of D3×AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×D3×D5⋊C8
unambiguous semidirect productD5⋊(C2×D3×C8)
unambiguous semidirect product(D3×D5)⋊(C2×C8)

Splittings

derived, HallC3×C5 ⋊ C23×C8
SylowC5 ⋊ C22×D3×C8
SylowC3 ⋊ C22×D5⋊C8

Subgroups

subgroupG/H
center, hypercenterC2×C4D3×AGL(1,𝔽5)
commutator, hypocenterC3×C5C23×C8
FrattiniC2C22×D3×AGL(1,𝔽5)
FittingC2×C3×C4×C5C2×C4
socleC22×C3×C5C22×C4
prime radicalC22×D3×D5C4
cosocleC3×Dic5C24
LCSG ▷ C3×C5
UCSC1 ◁ C2×C4

676 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×(C2×AGL(1,𝔽5))⋊C8, #14294376, D3×#64874, …
maximal normal subgroup ofD3×(C2×AGL(1,𝔽5))⋊C8, #14294376, D3×#64874, …
maximal quotient ofC2×C4×D3×#170, C2×C4×#6738, C2×Dic3×D5⋊C8, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 11009);