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 |
| direct product | C7×#21556 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#41 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
874 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(8,9,11,10)(12,13,18,23)(14,24,26,35)(15,29,31,37)(16,22,17,21)(19,28,34,27)(20,32,36,30)(25,39,40,33)(38,42,43,41);(12,14,16,27,18,26,17,28)(13,19,21,24,23,34,22,35)(15,25,30,41,31,40,32,42)(20,33,29,38,36,39,37,43);(12,15)(13,20)(14,25)(16,30)(17,32)(18,31)(19,33)(21,29)(22,37)(23,36)(24,38)(26,40)(27,41)(28,42)(34,39)(35,43);(8,10,11,9)(14,26)(19,34)(24,35)(25,40)(27,28)(33,39)(38,43)(41,42)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14544);