Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C43×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#10693 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C7 | C23 |
| commutator | C22 | C43×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| socle, prime radical | C24×C7 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C7 ◁ G | |
1222 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(20,21,22,25,23,24,26,27);(9,11)(12,13,14,15);(16,17,18,19)(21,24)(25,27)784 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3681);