Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1902 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#10786 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #386 |
| commutator | C2×C4 | C2×C42×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| prime radical | C24×C7 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1178 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(12,13,17,23,18,21,16,22)(14,19,26,33,25,34,31,37)(15,27,29,20,30,36,28,35)(24,38,40,42,39,43,41,32);(9,11)(12,14)(13,19,21,34)(15,24)(16,26)(17,31)(18,25)(20,32,35,42)(22,33,23,37)(27,38,36,43)(28,40)(29,41)(30,39);(12,15,18,30)(13,20,21,35)(14,24,25,39)(16,29,17,28)(19,32,34,42)(22,36,23,27)(26,41,31,40)(33,43,37,38)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3774);