Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7×C8 · Schur multiplier (H2) = C23 |
| direct product | C7×#12653 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C7×C8 | C23 |
| commutator | C22 | C2×C4×C7×C8 |
| Frattini, cosocle | C22×C8 | C23×C7 |
| socle, prime radical | C23×C7 | C22×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7×C8 ◁ G | |
414 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,10,11)(12,13,15,14);(9,11)(16,17,18,22,19,23,24,29,20,21,25,27,26,28,30,31);(12,14,15,13)(17,21)(22,27)(23,28)(29,31)784 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 5641);