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C3×C4×C8×AGL(1,𝔽5) #14294188

order1920
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C3×C42×C8 · Schur multiplier (H2) = C43

Aliases

direct productC3×C4×C8×AGL(1,𝔽5)

Splittings

FittingC3×C4×C5×C8 ⋊ C4
derived, SylowC5 ⋊ C3×C42×C8
HallC3×C5 ⋊ C42×C8

Subgroups

subgroupG/H
center, hypercenterC3×C4×C8AGL(1,𝔽5)
commutator, hypocenterC5C3×C42×C8
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C4×C5×C8C4
socleC22×C3×C5C2×C42
prime radicalC22×C3×D5C22×C4
cosocleC2×C4×D5C23×C3
LCSG ▷ C5
UCSC1 ◁ C3×C4×C8

816 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 19886);