Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3026 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#20612 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | C2×#120 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | C2×#379 |
| prime radical | C2×C7×#585 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G | |
3640 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,12,17,13,16,25,30)(10,18,21,31,20,14,24,27)(11,15,23,29,22,28,35,38)(19,26,34,37,33,32,36,39);(8,10)(9,14)(11,19)(12,24)(13,20)(15,26)(16,18)(17,31)(21,25)(22,33)(23,36)(27,30)(28,32)(29,39)(34,35)(37,38);(8,11)(9,15)(10,19)(12,23)(13,22)(14,26)(16,28)(17,29)(18,32)(20,33)(21,34)(24,36)(25,35)(27,37)(30,38)(31,39);(9,16)(14,18)(15,28)(17,30)(26,32)(27,31)(29,38)(37,39)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13600);