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#13015472

order1280
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

No aliases for this group.

Splittings

SylowC5 ⋊ #7892

Subgroups

subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC4×C5C2×C4×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC4×C5×C4⋊C4C4
socleC23×C5C2×C22⋊C4
prime radicalC23×D5C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC4×C4⋊C4AGL(1,𝔽5)
hypocenterC5#7892
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Polycyclic presentation:

2^8,5|a^2=e,b^2=f,c^2=g,d^2=g,e^2=h,f^2=gh,b^a=bd,d^a=dg,f^a=fg,i^a=i^3,c^b=cg,i^b=i^2,i^c=i^4,i^e=i^4,i^f=i^4

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1085740);