Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25140 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#25145 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3005 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
996 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)(8,9)(10,11)(12,13,18,31,17,22,16,21)(14,19,32,43,25,35,24,34)(15,26,28,20,30,37,29,38)(23,39,40,33,27,42,41,36);(9,11)(12,14,16,24,17,25,18,32)(13,19,21,34,22,35,31,43)(15,27,29,40,30,23,28,41)(20,36,26,42,38,33,37,39);(12,15)(13,20)(14,23)(16,28)(17,30)(18,29)(19,33)(21,37)(22,38)(24,40)(25,27)(26,31)(32,41)(34,42)(35,36)(39,43);(9,11)(12,16,17,18)(13,21,22,31)(14,24,25,32)(15,28,30,29)(19,34,35,43)(20,37,38,26)(23,40,27,41)(33,42,36,39)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 18133);