Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#21494 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C23×C7 | C23×C4 |
| prime radical | C7×#392 | C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
1038 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)(9,11)(12,13)(14,15)(16,17,21,19,20,23,28,27)(18,22,26,25,24,29,31,30);(8,9,10,11)(16,18)(17,22)(19,25)(20,24)(21,26)(23,29)(27,30)(28,31);(13,15)(17,23)(18,24)(19,27)(26,31);(16,19,21,23,20,27,28,17)(18,25,26,29,24,30,31,22)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14482);