Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3068 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25×C4 |
| direct product | C7×#21250 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1434 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)(9,11)(12,13,17,22,18,21,16,30)(14,19,25,34,24,35,31,33)(15,26,29,36,27,40,28,20)(23,37,39,32,38,43,41,42);(8,9,10,11)(12,14,16,25,18,24,17,31)(13,19,22,33,21,35,30,34)(15,23,28,39,27,38,29,41)(20,32,26,37,36,42,40,43);(12,15,16,28,18,27,17,29)(13,20,22,26,21,36,30,40)(14,23,25,39,24,38,31,41)(19,32,33,37,35,42,34,43);(15,27)(20,36)(23,38)(26,40)(28,29)(32,42)(37,43)(39,41)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14238);