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D5⋊(C4⋊(C3⋊C16)) #14314305

order1920
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

unambiguous semidirect productD5⋊(C4⋊(C3⋊C16))

Splittings

HallC3×C5 ⋊ C2×C4⋊C16
SylowC5 ⋊ C2×C4⋊(C3⋊C16)
SylowC3 ⋊ D5⋊(C4⋊C16)

Subgroups

subgroupG/H
centerC2×C8C2×ΓL(1,𝔽16)
commutatorC2×C3×C5C22×C16
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C4×C5×C8C4
socleC22×C3×C5C22×C8
prime radicalC22×C3×D5C2×C8
cosocleC2×C3×#168C23
hypercenterC4×C8ΓL(1,𝔽16)
hypocenterC3×C5C2×C4⋊C16
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C8 ◁ C4×C8

368 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Polycyclic presentation:

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

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 40003);