Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11858 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#11894 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#102 |
| commutator | C2×C8 | C22×C4×C7 |
| Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C7×#3050 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ C23×C7×C8 ◁ G | |
394 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,14,15,12)(11,13)(16,17,21,27,23,29,22,28)(18,30,33,45,35,46,34,41)(19,36,20,39,38,26,37,25)(24,40,42,32,44,31,43,47);(8,10)(9,12)(11,15)(13,14)(16,18)(17,24)(19,32)(20,40)(21,34)(22,33)(23,35)(25,30)(26,45)(27,43)(28,42)(29,44)(31,37)(36,41)(38,47)(39,46);(10,15)(12,14)(16,19,22,37,23,38,21,20)(17,25,27,36,29,39,28,26)(18,31,34,32,35,40,33,47)(24,41,42,30,44,45,43,46)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 4882);