Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#21075 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | #121 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C22×C7 | C2×#121 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C23×C4×C7 ◁ G | |
1014 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(8,9,11,10)(12,13)(14,23)(15,28)(16,21)(17,32)(18,22)(19,26)(20,31)(24,38)(25,34)(27,37)(29,43)(30,35)(33,39)(36,41)(40,42);(8,10,11,9)(12,14,17,26,18,27,16,25)(13,19,21,23,22,34,32,37)(15,24,30,40,31,41,29,39)(20,33,35,36,28,42,43,38);(12,15,17,30,18,31,16,29)(13,20,21,35,22,28,32,43)(14,24,26,40,27,41,25,39)(19,33,23,36,34,42,37,38);(12,16,18,17)(13,21,22,32)(14,25,27,26)(15,29,31,30)(19,23,34,37)(20,35,28,43)(24,39,41,40)(33,36,42,38)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14063);