Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×C7×#1454 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C7 | C23 |
| commutator | C22 | C22×C42×C7 |
| Frattini, cosocle | C42 | C24×C7 |
| socle | C23×C7 | C2×C42 |
| prime radical | C24×C7 | C42 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C7 ◁ G | |
802 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2)(35,36,37,38,39,40,41);(3,4,6,10,7,9,13,16)(5,8,12,14,11,15,17,18)(19,20)(21,24)(22,26)(23,25)(27,31)(28,30)(29,32)(33,34);(3,5)(4,8)(6,12)(7,11)(9,15)(10,14)(13,17)(16,18)(19,21,22,27,23,28,29,33)(20,24,26,31,25,30,32,34);(4,9)(5,11)(10,16)(12,17)(20,25)(24,30)(26,32)(31,34)784 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 10310);