Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #468 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#21548 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C7×C8 | C2×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C22×C7 | C2×C4×D4 |
| prime radical | C7×#3054 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7×C8 ◁ C23×C7×C8 ◁ G | |
914 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(12,13,17,21,18,22,16,31)(14,23,27,32,24,36,26,19)(15,20,29,34,30,35,28,41)(25,37,40,42,38,43,39,33);(12,14,16,26,18,24,17,27)(13,19,21,23,22,32,31,36)(15,25,28,39,30,38,29,40)(20,33,34,37,35,42,41,43);(9,11)(14,24)(19,32)(23,36)(25,38)(26,27)(33,42)(37,43)(39,40);(12,15,17,29,18,30,16,28)(13,20,21,34,22,35,31,41)(14,25,27,40,24,38,26,39)(19,33,23,37,32,42,36,43)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14536);