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AGL(1,𝔽5)×#815 #14294224

order1920
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C2×C42

Aliases

direct productAGL(1,𝔽5)×#815

Splittings

HallC3×C5 ⋊ C4×#97
SylowC5 ⋊ C4×#815
SylowC3 ⋊ AGL(1,𝔽5)×#97

Subgroups

subgroupG/H
center, FrattiniC2×C4C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C43
FittingC2×C3×C5×C8C2×C4
socleC22×C3×C5C2×C42
prime radicalC22×C3×D5C22×C4
cosocleC2×C3×C4×D5C23
hypercenterC2×C8D3×AGL(1,𝔽5)
hypocenterC3×C5C4×#97
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C8

720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×#97
maximal normal subgroup ofD3×AGL(1,𝔽5)×#97

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 19922);