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AGL(1,𝔽5)×#121 #10617249

order640
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productAGL(1,𝔽5)×#121

Splittings

FittingC5×#121 ⋊ C4
SylowC5 ⋊ C4×#121

Subgroups

subgroupG/H
center, FrattiniC22C23×AGL(1,𝔽5)
commutator, socleC22×C5C23×C4
FittingC5×#121C4
prime radicalD5×#121C2
cosocleC22×D5C24
hypercenter#121AGL(1,𝔽5)
hypocenterC5C4×#121
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #121

824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#327, #13017032, #13017042, …
maximal normal subgroup ofAGL(1,𝔽5)×#327, #13017032, #13017042, …
maximal quotient ofAGL(1,𝔽5)×#386, AGL(1,𝔽5)×#388, AGL(1,𝔽5)×#390, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(640, 19331);