Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C5 · Schur multiplier (H2) = C212×C4 |
| direct product | C2×C5×#3549 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
8802 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 6 generators on 23 points:
(1,2)(19,20,21,22,23);(4,6)(8,9)(12,15)(13,14);(3,4,7,6)(5,9,10,8)(11,12,16,15)(13,18,14,17);(11,13,16,14)(12,17,15,18);(3,5,7,10)(4,8,6,9)(11,14,16,13)(12,18,15,17);(3,6,7,4)(5,9,10,8)(11,15,16,12)(13,18,14,17)380 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 55745);