Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17367 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#20730 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C24×C7 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C7×#117 ◁ G | |
1166 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,12)(14,15)(16,17,20,25,21,24,33,38)(18,22,28,36,27,35,43,46)(19,29,30,39,31,23,32,37)(26,40,42,47,41,34,44,45);(9,12)(13,15)(16,18)(17,22)(19,26)(20,28)(21,27)(23,34)(24,35)(25,36)(29,40)(30,42)(31,41)(32,44)(33,43)(37,45)(38,46)(39,47);(16,19,21,31)(17,23,24,29)(18,26,27,41)(20,32,33,30)(22,34,35,40)(25,39,38,37)(28,44,43,42)(36,47,46,45);(8,10,11,14)(9,13,12,15)(18,27)(22,35)(26,41)(28,43)(34,40)(36,46)(42,44)(45,47)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13718);