Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23912 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#23914 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3485 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1706 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)(12,13,17,21)(14,18,23,33)(15,25,26,37)(16,28,31,20)(19,30,35,27)(22,38,39,42)(24,36,29,34)(32,41,43,40);(8,9)(10,11)(12,14,17,23)(13,18,21,33)(15,22,26,39)(16,29,31,24)(19,32,35,43)(20,36,28,34)(25,42,37,38)(27,41,30,40);(9,11)(12,15)(13,19)(14,22)(16,30)(17,26)(18,32)(20,37)(21,35)(23,39)(24,41)(25,28)(27,31)(29,40)(33,43)(34,42)(36,38);(14,23)(16,31)(18,33)(20,28)(22,39)(25,37)(27,30)(32,43)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16902);