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C4×#41×AGL(1,𝔽5) #13043832

order1280
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC4×#41×AGL(1,𝔽5)

Splittings

FittingC4×C5×#41 ⋊ C4
SylowC5 ⋊ C42×#41

Subgroups

subgroupG/H
centerC42C22×AGL(1,𝔽5)
commutatorC2×C5C23×C42
FrattiniC22C24×AGL(1,𝔽5)
FittingC4×C5×#41C4
socleC22×C5C24×C4
prime radicalC2×D5×#41C22
cosocleC22×D5C25
hypercenterC4×#41AGL(1,𝔽5)
hypocenterC5C42×#41
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C42 ◁ C4×#41

4086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#3498, AGL(1,𝔽5)×#1906, C4×#41×#1043, …
maximal normal subgroup ofAGL(1,𝔽5)×#3498, AGL(1,𝔽5)×#1906, AGL(1,𝔽5)×#2875, …
maximal quotient ofC4×#41×#1043, C4×#13107559, C2×C4×#41×AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114100);