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AGL(1,𝔽5)×#940 #14322287

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productAGL(1,𝔽5)×#940

Splittings

FittingC2×C3×C5×D4 ⋊ C2×C4
HallC3×C5 ⋊ C4×#127
SylowC5 ⋊ C4×#940
SylowC3 ⋊ AGL(1,𝔽5)×#127

Subgroups

subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×D4C2×C4
prime radicalD5×#940C2
cosocleC22×C3×D5C24
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5C4×#127
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

1848 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×#127, AGL(1,𝔽5)×#5198, AGL(1,𝔽5)×#5241, …
maximal normal subgroup ofD3×AGL(1,𝔽5)×#127, AGL(1,𝔽5)×#5198, AGL(1,𝔽5)×#5241, …
maximal quotient of#940×#1043, AGL(1,𝔽5)×#64149

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 47985);