Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18316 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18342 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3459 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
998 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(9,13)(10,11)(14,15)(16,17,20,23)(18,24,26,31)(19,27,29,22)(21,28,30,25);(8,9)(10,13)(11,15)(12,14)(16,18)(17,21)(19,28)(20,26)(22,31)(23,30)(24,27)(25,29);(19,29)(22,27)(24,31)(25,28);(8,10,12,11)(9,13,14,15)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11330);