Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7654 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C4 |
| direct product | C7×#7669 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C43×C7 ◁ G | |
384 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(9,12,13,14)(16,17,20,23,21,18,19,22)(24,25)(26,32,34,29)(27,30)(28,31)(33,38,39,36)(35,37);(8,9,11,13)(10,14,15,12)(16,18,21,17)(19,22,20,23)(24,26)(25,29)(27,33)(28,34)(30,36)(31,32)(35,39)(37,38);(16,19,21,20)(17,22,18,23)(24,27,28,35)(25,30,31,37)(26,33,34,39)(29,36,32,38)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 657);