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C8×AGL(1,𝔽16) #14512434

order1920
isoclinismisoclinic class of AGL(1,𝔽16)
automorphism?
homologyAbelianization (H1) = C3×C5×C8 · Schur multiplier (H2) = C1

Aliases

direct productC8×AGL(1,𝔽16)
unambiguous semidirect product(C8×C22⋊A4)⋊C5
unambiguous semidirect product(C8×C24⋊C5)⋊C3

Splittings

Fitting, SylowC24×C8 ⋊ C3×C5
derivedC24 ⋊ C3×C5×C8
HallC8×C24⋊C5 ⋊ C3
HallC8×C22⋊A4 ⋊ C5

Subgroups

subgroupG/H
center, hypercenterC8AGL(1,𝔽16)
commutator, hypocenterC24C3×C5×C8
FrattiniC4C2×AGL(1,𝔽16)
FittingC24×C8C3×C5
socleC25C3×C4×C5
prime radicalC2×AGL(1,𝔽16)C4
cosocleC24×C4C2×C3×C5
LCSG ▷ C24
UCSC1 ◁ C8

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 238132);