Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C7×#62810 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| socle | C22×C7 | C26 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ G | |
7220 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)(8,9)(10,13)(11,12)(14,15)(16,17)(18,22)(19,26)(20,29)(21,24)(23,27)(25,31)(28,30);(9,12)(13,15)(16,18,21,20)(17,22,24,29)(19,25,27,28)(23,30,26,31);(16,19)(17,23)(18,25)(20,28)(21,27)(22,30)(24,26)(29,31);(19,27)(23,26)(25,28)(30,31);(16,20,21,18)(17,22,24,29)(19,28,27,25)(23,30,26,31);(8,10,11,14)(9,13,12,15)616 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55798);