Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C52 · Schur multiplier (H2) = C25×C5 |
| direct product | C52×#548 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C52 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C52 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C52 ◁ G | |
1160 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 800 |
A minimal faithful permutation representation — 4 generators on 22 points:
(1,2,3,4,5)(12,14)(16,19)(20,21);(6,7,8,9,10)(15,16,18,19)(17,21,22,20);(11,12)(13,14);(15,17,18,22)(16,20,19,21)625 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9758);