Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | C7×#23368 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle, prime radical | C23×C7 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
580 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,13)(12,15)(16,17)(18,25)(19,23)(20,29)(21,24)(22,28)(26,31)(27,30)(32,33,36,39,35,38,43,46)(34,40,42,47,41,37,44,45);(10,15)(12,14)(16,18,21,28)(17,22,24,25)(19,27,20,26)(23,31,29,30);(8,10,11,15)(9,12,13,14)(16,19,21,20)(17,23,24,29)(18,26,28,27)(22,30,25,31)(32,34,35,41)(33,37,38,40)(36,42,43,44)(39,45,46,47);(9,13)(12,14)(16,20,21,19)(17,23,24,29)(18,27,28,26)(22,30,25,31)(34,41)(37,40)(42,44)(45,47)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16356);