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AGL(1,𝔽5)×#568 #13044402

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

Aliases

direct productAGL(1,𝔽5)×#568

Splittings

FittingC5×#568 ⋊ C4
SylowC5 ⋊ C4×#568

Subgroups

subgroupG/H
center, FrattiniC4C24×AGL(1,𝔽5)
commutator, socleC2×C5C23×C42
FittingC5×#568C4
prime radicalC2×D5×#41C22
cosocleC4×D5C25
hypercenter#568AGL(1,𝔽5)
hypocenterC5C4×#568
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C4 ◁ #568

3250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72221166, AGL(1,𝔽5)×#3585, AGL(1,𝔽5)×#1891, …
maximal normal subgroup ofAGL(1,𝔽5)×#3585, AGL(1,𝔽5)×#1891, AGL(1,𝔽5)×#1914, …
maximal quotient of#72221166, #72221592, #72223261, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114670);