Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C52 · Schur multiplier (H2) = C2×C4×C5 |
| direct product | C52×#124 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C52 | C23 |
| commutator, Frattini, cosocle | C22 | C23×C52 |
| prime radical | C2×C52×D4 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C52 ◁ G | |
304 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 400 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,2,3,4,5)(12,13)(17,21)(19,22);(6,7,8,9,10)(11,12,14,13)(15,16,18,20)(17,19,21,22);(11,13,14,12)(15,17)(16,19)(18,21)(20,22)350 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 943);