Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C7×#62851 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
7066 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 6 generators on 31 points:
(1,2,3,4,5,6,7)(9,12)(13,15)(16,17)(18,21)(19,20)(22,30)(23,25)(24,31)(26,27)(28,29);(8,9,11,12)(10,13,14,15)(16,18,23,20)(17,19,25,21)(22,26,31,28)(24,27,30,29);(16,19,23,21)(17,18,25,20)(22,27,31,29)(24,26,30,28);(16,20,23,18)(17,19,25,21)(22,28,31,26)(24,27,30,29);(8,10,11,14)(9,13,12,15)(16,21,23,19)(17,18,25,20)(22,29,31,27)(24,26,30,28);(16,22)(17,24)(18,26)(19,27)(20,28)(21,29)(23,31)(25,30)574 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55839);