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ΓL(1,𝔽16)⋊C16 #11746449

order960
isoclinismisoclinic class of D3×AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C16 · Schur multiplier (H2) = C4

Aliases

unambiguous semidirect productΓL(1,𝔽16)⋊C16

Splittings

derived, HallC3×C5 ⋊ C4×C16
SylowC5 ⋊ Dic3×C16
SylowC3 ⋊ C16×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, Frattini, hypercenterC8D3×AGL(1,𝔽5)
commutator, hypocenterC3×C5C4×C16
FittingC3×C5×C8C2×C4
socleC2×C3×C5C4×C8
prime radicalC2×C3×D5C2×C8
cosocleC3×C8×D5C22
LCSG ▷ C3×C5
UCSC1 ◁ C8

116 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Polycyclic presentation:

2^6,3,5|a^2=c,b^2=d,c^2=e,d^2=e,e^2=f,h^a=h^2,g^b=g^2,h^c=h^4

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C16×AGL(1,𝔽5), C2×ΓL(1,𝔽16)⋊C16, #14312613, …
maximal normal subgroup ofD3×C16×AGL(1,𝔽5), C2×ΓL(1,𝔽16)⋊C16, #14312613, …
maximal quotient of#14277448, #14277484, #14278694, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 644);