Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1913 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#10941 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | #386 |
| commutator | C23 | C2×C42×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| socle | C2×C7 | #1437 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G | |
904 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,12,17,13,16,24,30)(10,14,20,27,19,26,23,31)(11,15,22,28,21,29,35,39)(18,32,34,38,33,25,36,37);(8,10)(9,14,16,26)(11,18)(12,23)(13,19)(15,25,29,32)(17,31,30,27)(20,24)(21,33)(22,36)(28,38,39,37)(34,35);(8,11,12,22,13,21,24,35)(9,15,17,28,16,29,30,39)(10,18,23,36,19,33,20,34)(14,25,31,38,26,32,27,37)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3929);