Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #20338 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#20338 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | C22×C42 |
| commutator | C4 | C22×C42×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | C22×#95 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ G | |
2036 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)(10,18,21,31)(11,15)(12,16)(13,17)(14,20,26,34)(19,30,32,38)(22,27)(23,28)(24,29)(25,33,36,39)(35,37);(8,10)(9,14,17,26)(11,19)(12,20)(13,21)(15,25,27,36)(16,18,29,31)(22,32)(23,33)(24,34)(28,30,37,38)(35,39);(8,11)(9,15)(10,19)(12,23)(13,22)(14,25)(16,28)(17,27)(18,30)(20,33)(21,32)(24,35)(26,36)(29,37)(31,38)(34,39);(11,22)(15,27)(19,32)(23,35)(25,36)(28,37)(30,38)(33,39)574 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13326);