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AGL(1,𝔽5)×#901 #14411499

order1920
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productAGL(1,𝔽5)×#901

Splittings

FittingC2×C3×C5×C8 ⋊ C2×C4
HallC3×C5 ⋊ C4×#131
SylowC5 ⋊ C4×#901
SylowC3 ⋊ AGL(1,𝔽5)×#131

Subgroups

subgroupG/H
centerC8C2×D3×AGL(1,𝔽5)
commutator, socleC2×C3×C5C22×C42
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC2×C3×C5×C8C2×C4
prime radicalD5×#235C22
cosocleC3×C4×D5C24
hypercenterC2×C8D3×AGL(1,𝔽5)
hypocenterC3×C5C4×#131
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C8 ◁ C2×C8

1144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

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, 137197);