Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | C5×#3534 ⋊ C2 |
| Sylow | C5 ⋊ #62729 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D5 |
| commutator, socle, cosocle | C22×C5 | C26 |
| Fitting | C5×#3534 | C2 |
| hypercenter | #3534 | D5 |
| hypocenter | C5 | #62729 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ #3534 | |
7346 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|f^2=g,b^a=bg,c^a=ch,d^a=dg,e^a=eh,c^b=cg,d^b=dh,i^d=i^4,i^f=i^4152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1076873);