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#13035245

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

Aliases

No aliases for this group.

Splittings

FittingC5×#418 ⋊ C4
SylowC5 ⋊ #21091

Subgroups

subgroupG/H
centerC22C2×D4×AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC5×#418C4
socleC22×C5C2×C4×D4
prime radicalC22×D4×D5C22
cosocleC2×C4×D5C24
hypercenter#418AGL(1,𝔽5)
hypocenterC5#21091
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

1234 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Polycyclic presentation:

2^8,5|a^2=g,b^2=egh,c^2=e,e^2=h,f^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,i^a=i^3,i^b=i^2,d^c=dh,i^g=i^4

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#3058, #72269149
maximal normal subgroup ofAGL(1,𝔽5)×#3058
maximal quotient of#72269149

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1105513);