Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#10286 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C7×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
542 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7)(9,13)(10,14)(11,15)(16,17)(18,26)(19,23)(20,29)(21,25)(22,27)(24,30)(28,31);(8,9)(10,12)(11,14)(13,15)(16,18,21,19)(17,22,25,31)(20,28,30,27)(23,29,26,24);(8,10,12,9)(11,13,15,14)(16,19,21,18)(17,23,25,26)(20,27,30,28)(22,24,31,29)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3274);