Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C5×#1781 ⋊ C2 |
| Sylow | C5 ⋊ #23900 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#4028 |
| commutator, cosocle | C24×C5 | C24 |
| Frattini | C24 | C23×D5 |
| Fitting | C5×#1781 | C2 |
| socle | C22×C5 | C2×#120 |
| hypercenter | #1781 | D5 |
| hypocenter | C5 | #23900 |
| LCS | G ▷ C24×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C25 ◁ #1781 | |
3520 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|b^a=be,c^a=cf,d^a=de,i^a=i^4,c^b=cg,f^b=fh,e^c=eh,i^c=i^4,f^d=fh110 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#23900, #72242893, #72242897, … |
| maximal normal subgroup of | D5×#23900, #72242893, #72242897, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 201150);