Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1468 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | C7×#7916 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| prime radical | C24×C7 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C22×C42×C7 ◁ G | |
622 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7)(12,13)(14,20,22,17)(15,18)(16,19)(21,26,27,24)(23,25)(28,29,31,35,32,34,40,42)(30,36,38,43,37,33,39,41);(8,9,10,11)(12,14)(13,17)(15,21)(16,22)(18,24)(19,20)(23,27)(25,26)(28,30)(29,33)(31,39)(32,37)(34,36)(35,43)(38,40)(41,42);(12,15,16,23)(13,18,19,25)(14,21,22,27)(17,24,20,26)(30,37)(33,36)(38,39)(41,43)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 904);