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AGL(1,𝔽5)×#392 #13028084

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

Aliases

direct productAGL(1,𝔽5)×#392

Splittings

FittingC5×#392 ⋊ C4
SylowC5 ⋊ C4×#392

Subgroups

subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutator, socleC23×C5C23×C4
FittingC5×#392C4
prime radicalD5×#392C2
cosocleC23×D5C24
hypercenter#392AGL(1,𝔽5)
hypocenterC5C4×#392
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #392

3502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#2403, AGL(1,𝔽5)×#2433, AGL(1,𝔽5)×#2669, …
maximal normal subgroup ofAGL(1,𝔽5)×#2403, AGL(1,𝔽5)×#2433, AGL(1,𝔽5)×#2669, …
maximal quotient ofAGL(1,𝔽5)×#2010, AGL(1,𝔽5)×#2002, AGL(1,𝔽5)×#2008, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1098352);