Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C5×#3026 ⋊ C2 |
| Sylow | C5 ⋊ #60399 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D5×#120 |
| commutator, cosocle | C23×C5 | C25 |
| Frattini | C23 | C24×D5 |
| Fitting | C5×#3026 | C2 |
| socle | C2×C5 | C22×#120 |
| hypercenter | #3026 | D5 |
| hypocenter | C5 | #60399 |
| LCS | G ▷ C23×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2 ◁ C24 ◁ #3026 | |
5128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|b^a=bf,c^a=cg,i^a=i^4,g^b=gh,f^c=fh,e^d=eh,i^e=i^4116 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#60399, #72253562, #72253568 |
| maximal normal subgroup of | D5×#60399, #72253562, #72253568 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1036320);