Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1462 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#10801 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C7 |
| Frattini, cosocle | C25 | C23×C7 |
| prime radical | C25×C7 | C23 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C24×C4×C7 ◁ G | |
1194 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3,4,5,6,7)(13,14)(16,17)(18,22,23,20)(19,21);(8,9,10,11)(12,13,15,14);(12,14,15,13)(16,18)(17,20)(19,23)(21,22)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3789);