Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18746 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18771 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C2×C7×#550 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
1234 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)(8,9,12,15)(10,13,11,14)(16,17,21,24)(18,25,27,30)(19,23,20,28)(22,29,31,26);(9,13)(10,11)(14,15)(16,18)(17,22)(19,26)(20,29)(21,27)(23,30)(24,31)(25,28);(9,14)(10,11)(13,15)(16,19,21,20)(17,23,24,28)(18,26,27,29)(22,30,31,25);(9,15)(13,14)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11759);