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AGL(1,𝔽5)×#874 #14322290

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

Aliases

direct productAGL(1,𝔽5)×#874

Splittings

FittingC3×C42×C5 ⋊ C2×C4
HallC3×C5 ⋊ C4×#127
SylowC5 ⋊ C4×#874
SylowC3 ⋊ AGL(1,𝔽5)×#127

Subgroups

subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C42×C5C2×C4
prime radicalD5×#874C2
cosocleC22×C3×D5C24
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5C4×#127
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

1848 conjugacy classes of subgroups; only the 318 normal subgroups are shown.

normal subgroups only

This group has 1848 conjugacy classes of subgroups — too many to draw. Only its 318 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×#127, AGL(1,𝔽5)×#4822, #874×#1043, …
maximal normal subgroup ofD3×AGL(1,𝔽5)×#127, AGL(1,𝔽5)×#4822
maximal quotient of#874×#1043, AGL(1,𝔽5)×#64083

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 47988);