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AGL(1,𝔽5)×C4⋊(C3⋊C8) #14296129

order1920
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productAGL(1,𝔽5)×C4⋊(C3⋊C8)

Splittings

HallC3×C5 ⋊ C4×C4⋊C8
SylowC5 ⋊ C4×C4⋊(C3⋊C8)
SylowC3 ⋊ AGL(1,𝔽5)×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C4C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C2×C4×C8
FittingC3×C42×C5C2×C4
socleC22×C3×C5C2×C42
prime radicalC22×C3×D5C22×C4
cosocleC2×C3×C4×D5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5C4×C4⋊C8
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42

632 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21827);