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AGL(1,𝔽5)×#407 #13033270

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productAGL(1,𝔽5)×#407

Splittings

FittingC5×#407 ⋊ C4
SylowC5 ⋊ C4×#407

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×AGL(1,𝔽5)
commutator, socleC22×C5C22×C42
FittingC5×#407C4
prime radicalC24×D5C2×C4
cosocleC2×C4×D5C24
hypercenter#407AGL(1,𝔽5)
hypocenterC5C4×#407
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ #407

2246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#1891, AGL(1,𝔽5)×#3003, AGL(1,𝔽5)×#2010, …
maximal normal subgroup ofAGL(1,𝔽5)×#1891, AGL(1,𝔽5)×#3003, AGL(1,𝔽5)×#2010, …
maximal quotient of#72221686, #72223273, AGL(1,𝔽5)×#1490

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103538);