Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13331 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#13446 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #459 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C2×C7×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C2×C4×C7×C8 ◁ G | |
396 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)(14,26)(15,33)(16,23)(17,22)(18,35)(19,38)(20,25)(21,28)(24,36)(27,29)(30,42)(31,34)(32,43)(37,41)(39,40);(12,14,20,32)(13,21,25,42)(15,34,22,40)(16,29,18,37)(17,28,33,30)(19,39,36,31)(23,26,35,43)(24,27,38,41);(9,11)(12,15,16,24,36,23,33,13,20,22,18,38,19,35,17,25)(14,27,28,34,39,42,37,43,32,41,30,40,31,21,29,26)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6434);