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AGL(1,𝔽5)×#427 #13033574

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productAGL(1,𝔽5)×#427

Splittings

FittingC5×#427 ⋊ C4
SylowC5 ⋊ C4×#427

Subgroups

subgroupG/H
centerC2×C4D4×AGL(1,𝔽5)
commutatorC4×C5C22×C42
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC5×#427C4
socleC22×C5C2×C4×D4
prime radicalC23×D5C2×D4
cosocleC2×C4×D5C24
hypercenter#427AGL(1,𝔽5)
hypocenterC5C4×#427
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

1182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#3058, #72242511, AGL(1,𝔽5)×#2943, …
maximal normal subgroup ofAGL(1,𝔽5)×#3058, AGL(1,𝔽5)×#2943, AGL(1,𝔽5)×#2912, …
maximal quotient of#72242511

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103842);