Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C23×C42 |
| direct product | C7×#14528 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C7 | C24 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C24 | C24×C7 |
| prime radical | C23×C7×D4 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
1758 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(12,13,15,14)(16,17,19,20)(18,21,22,23)(24,25,27,30)(26,29,31,28);(9,11)(17,20)(18,22)(24,26,27,31)(25,28,30,29);(8,9)(10,11)(12,14,15,13)(16,17)(18,21)(19,20)(22,23)(24,26)(25,29)(27,31)(28,30);(16,18)(17,21)(19,22)(20,23)(24,25)(26,29)(27,30)(28,31)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 7516);