Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23876 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23956 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1284 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,13)(12,15)(16,17)(18,21)(19,27)(20,26)(22,24)(23,31)(25,29)(28,30);(8,10,11,15)(9,12,13,14)(16,18,21,17)(19,28,30,27)(20,26,22,24)(23,29,25,31);(16,19)(17,23)(18,25)(20,29)(21,30)(22,31)(24,28)(26,27);(9,13)(12,14)(16,20,21,22)(17,24,18,26)(19,29,30,31)(23,28,25,27)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16944);