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C22×C3×C8×AGL(1,𝔽5) #14411166

order1920
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C22×C3×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22×C3×C8×AGL(1,𝔽5)

Splittings

FittingC22×C3×C5×C8 ⋊ C4
derived, SylowC5 ⋊ C22×C3×C4×C8
HallC3×C5 ⋊ C22×C4×C8

Subgroups

subgroupG/H
center, hypercenterC22×C3×C8AGL(1,𝔽5)
commutator, hypocenterC5C22×C3×C4×C8
FrattiniC4C23×C3×AGL(1,𝔽5)
FittingC22×C3×C5×C8C4
socleC23×C3×C5C42
prime radicalC23×C3×D5C2×C4
cosocleC4×D5C24×C3
LCSG ▷ C5
UCSC1 ◁ C22×C3×C8

1520 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, 136864);