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×#62843 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| prime radical | C23×C7×D4 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
7130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 6 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,11,13)(10,14,15,12)(16,17)(18,22)(19,26)(20,21)(23,27)(24,28)(25,31)(29,30);(8,10,11,15)(9,12,13,14)(18,24)(22,28)(25,30)(29,31);(17,21)(22,28)(23,26)(29,31);(16,17)(18,22)(19,23)(20,21)(24,28)(25,29)(26,27)(30,31);(16,18)(17,22)(19,25)(20,24)(21,28)(23,29)(26,31)(27,30);(16,19)(17,23)(18,25)(20,27)(21,26)(22,29)(24,30)(28,31)574 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55831);