Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #34980 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C29 |
| direct product | C5×#34984 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C5 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
3690 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 5 generators on 21 points:
(1,2,3,4,5)(7,9)(11,12)(16,20)(19,21);(10,11,13,12)(15,18)(19,21);(6,7)(8,9)(10,12,13,11)(14,15)(16,19)(17,18)(20,21);(14,15)(16,19)(17,18)(20,21);(14,16)(15,19)(17,20)(18,21)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 27972);