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C32×C8×AGL(1,𝔽5) #13086243

order1440
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C32×C4×C8 · Schur multiplier (H2) = C3×C4

Aliases

direct productC32×C8×AGL(1,𝔽5)

Splittings

FittingC32×C5×C8 ⋊ C4
derived, SylowC5 ⋊ C32×C4×C8
HallC32×C5 ⋊ C4×C8

Subgroups

subgroupG/H
center, hypercenterC32×C8AGL(1,𝔽5)
commutator, hypocenterC5C32×C4×C8
FrattiniC4C2×C32×AGL(1,𝔽5)
FittingC32×C5×C8C4
socleC2×C32×C5C42
prime radicalC2×C32×D5C2×C4
cosocleC4×D5C22×C32
LCSG ▷ C5
UCSC1 ◁ C32×C8

264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 360

Conjugacy classes & character table

360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 2560);