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C2×AGL(1,𝔽5)×#99 #13033342

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×AGL(1,𝔽5)×#99

Splittings

FittingC2×C5×#99 ⋊ C4
SylowC5 ⋊ C2×C4×#99

Subgroups

subgroupG/H
centerC22C22⋊C4×AGL(1,𝔽5)
commutatorC22×C5C22×C42
FrattiniC23C23×AGL(1,𝔽5)
FittingC2×C5×#99C4
socleC22×C5C4×C22⋊C4
prime radicalC22×D4×D5C22
cosocleC23×D5C24
hypercenterC2×#99AGL(1,𝔽5)
hypocenterC5C2×C4×#99
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

2242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×B(4,𝔽2), C2×#72221652, #72221770, …
maximal normal subgroup ofC2×AGL(1,𝔽5)×B(4,𝔽2), AGL(1,𝔽5)×#2021, C2×AGL(1,𝔽5)×AΣL(1,𝔽16), …
maximal quotient ofC2×#72221652, #72221770, D3×AGL(1,𝔽5)×#99, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103610);