Finite Group Databasebeta

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D5⋊((C2×D3)⋊C16) #14312819

order1920
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C24

Aliases

unambiguous semidirect productD5⋊((C2×D3)⋊C16)

Splittings

HallC3×C5 ⋊ C2×C22⋊C16
SylowC5 ⋊ C2×(C2×D3)⋊C16
SylowC3 ⋊ D5⋊(C22⋊C16)

Subgroups

subgroupG/H
center, hypercenterC2×C8D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C16
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×C8C2×C4
socleC22×C3×C5C22×C8
prime radicalC22×D3×D5C8
cosocleC2×C3×#168C23
hypocenterC3×C5C2×C22⋊C16
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C8

544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Polycyclic presentation:

2^7,3,5|a^2=e,e^2=f,f^2=g,b^a=bd,i^a=i^2,h^b=h^2,i^c=i^4,i^e=i^4

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 38517);