Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C5×#400 ⋊ C2 |
| Sylow | C5 ⋊ #15940 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D5 |
| commutator, socle, cosocle | C24×C5 | C24 |
| Fitting | C2×C5×#400 | C2 |
| prime radical | C24×D5 | C23 |
| hypercenter | C2×#400 | D5 |
| hypocenter | C5 | #15940 |
| LCS | G ▷ C24×C5 ▷ C5 | |
| UCS | C1 ◁ C24 ◁ C2×#400 | |
1566 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=e,b^2=eg,c^2=e,d^2=eg,b^a=be,c^a=cf,d^a=dh,c^b=cg,d^b=de,i^c=i^4,i^d=i^4146 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 117001);