Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×C7×#2168 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C7×C8 | C23 |
| commutator | C22 | C23×C7×C8 |
| Frattini, cosocle | C2×C8 | C24×C7 |
| socle | C23×C7 | C22×C8 |
| prime radical | C22×C7×D4 | C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7×C8 ◁ G | |
754 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2)(23,24,25,26,27,28,29);(3,4)(5,6)(7,8,10,14,11,9,16,17,12,15,19,22,20,18,13,21);(4,6);(7,9,10,17,11,15,16,22,12,18,19,21,20,8,13,14)784 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 26418);