Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 184320 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C5 |
| abelian | C22×C52×C8 |
| multiplicative | (ℤ/1353)ˣ, (ℤ/1804)ˣ, (ℤ/2706)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C23×C52 |
| socle, prime radical | C23×C52 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
304 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 800 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,2,3,4,5,6,7,8)(13,14,15,16,17);(9,10)(18,19,20,21,22);(11,12)800 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 948);