Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C7 · Schur multiplier (H2) = C27 |
| direct product | C22×C7×#343 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C7 | C22⋊C4 |
| commutator | C22 | C22×C42×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C25×C7 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ C24×C4×C7 ◁ G | |
2494 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2)(17,18,19,20,21,22,23);(3,4);(9,10,11,14,12,13,15,16);(5,6,7,8)(10,13)(11,15)616 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13344);