Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2883 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#20360 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | C22×C22⋊C4 |
| commutator | C22 | C22×C42×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | C22×#95 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C22×C7×#41 ◁ G | |
1996 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)(10,18,20,14)(11,15)(12,17)(13,16)(19,30,32,25)(21,31,34,26)(22,27)(23,28)(24,29)(33,38,39,36)(35,37);(8,10,12,21,13,20,24,34)(9,14,17,26,16,18,29,31)(11,19,23,33,22,32,35,39)(15,25,28,36,27,30,37,38);(8,11)(9,15)(10,19)(12,23)(13,22)(14,25)(16,27)(17,28)(18,30)(20,32)(21,33)(24,35)(26,36)(29,37)(31,38)(34,39);(11,22)(15,27)(19,32)(23,35)(25,30)(28,37)(33,39)(36,38)574 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13348);