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AGL(1,𝔽5)×#361 #13025901

order1280
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productAGL(1,𝔽5)×#361

Splittings

FittingC5×#361 ⋊ C4
SylowC5 ⋊ C4×#361

Subgroups

subgroupG/H
centerC2AGL(1,𝔽5)×#102
commutatorC5×C8C2×C42
FrattiniC2×C8C22×AGL(1,𝔽5)
FittingC5×#361C4
socleC2×C5C4×#102
prime radicalC2×D5×D8C22
cosocleC2×C8×D5C23
hypercenter#361AGL(1,𝔽5)
hypocenterC5C4×#361
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

498 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 112 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) = 80

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×AGL(1,ℤ/16), #72220801, AGL(1,𝔽5)×#2213, …
maximal normal subgroup ofAGL(1,𝔽5)×AGL(1,ℤ/16), AGL(1,𝔽5)×#2213, C2×AGL(1,𝔽5)×#361, …
maximal quotient of#72220801, AGL(1,𝔽5)×#1333, C2×AGL(1,𝔽5)×#361, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1096169);