Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#11935 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#102 |
| commutator | C2×C8 | C22×C4×C7 |
| Frattini, cosocle | C4×C8 | C23×C7 |
| prime radical | C23×C7 | #102 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ C2×C4×C7×C8 ◁ G | |
302 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(13,15)(16,17,20,26,21,27,35,41,22,24,36,42,34,43,19,25)(18,28,30,38,31,44,29,45,32,46,33,23,37,39,47,40);(8,9,11,13)(10,15,14,12)(16,18)(17,23)(19,33)(20,29)(21,37)(22,32)(24,38)(25,44)(26,28)(27,45)(30,35)(31,34)(36,47)(39,41)(40,43)(42,46);(17,24)(23,38)(25,41)(26,42)(27,43)(28,46)(39,44)(40,45)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 4923);