Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C52×#499 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C52 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C52 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C52 ◁ C42×C52 ◁ G | |
344 conjugacy classes of subgroups.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 1600 |
A minimal faithful permutation representation — 3 generators on 34 points:
(1,2,3,4,5)(11,12,14,16)(13,17,18,15)(19,20,22,24)(21,27,28,34)(23,31,30,26)(25,33,32,29);(6,7,8,9,10)(11,13,14,18)(12,15,16,17)(20,24)(25,32)(26,31)(27,34);(19,21,23,29,22,28,30,33)(20,25,26,27,24,32,31,34)550 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5588);