Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C16 · Schur multiplier (H2) = C22 |
| direct product | C7×#13645 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C7×C16 | C23 |
| commutator | C22 | C22×C7×C16 |
| Frattini, cosocle | C2×C16 | C23×C7 |
| socle | C22×C7 | C22×C16 |
| prime radical | C2×C7×D4 | C16 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C7×C16 ◁ G | |
204 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(12,13,15,20,16,21,27,35,17,14,23,24,29,25,38,39,18,22,28,36,30,37,41,43,31,26,19,32,33,40,34,42);(9,11);(12,14,15,24,16,25,27,39,17,22,23,36,29,37,38,43,18,26,28,32,30,40,41,42,31,13,19,20,33,21,34,35)784 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6633);