Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#10441 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C2×C7×#459 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
492 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)(8,9)(10,12)(11,13)(14,15)(16,17)(18,25)(19,21)(20,24)(22,26)(23,28)(27,30)(29,31);(9,12)(13,14)(17,21)(18,26)(19,28)(22,30)(23,24)(25,29);(9,13)(11,15)(12,14)(16,18,19,27,20,26,28,31)(17,22,23,30,24,25,21,29)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3429);