Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| isoclinism | isoclinic class of (C24⋊C5)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| derived | C24⋊C5 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | (C24⋊C5)⋊C2 |
| commutator, hypocenter | C24⋊C5 | C16 |
| Fitting | C24×C8 | D5 |
| socle | C25 | #168 |
| prime radical | C2×C24⋊C5 | C8 |
| cosocle | C8×C24⋊C5 | C2 |
| LCS | G ▷ C24⋊C5 | |
| UCS | C1 ◁ C8 | |
217 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2,5,2^7|a^2=g,g^2=h,h^2=i,b^a=b^4,c^a=cdef,d^a=df,e^a=ef,c^b=f,d^b=cf,e^b=cdf,f^b=cdef80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116371);