Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62817 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C7×#62820 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
7382 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)(9,12)(13,15)(16,17)(18,24)(19,25)(20,23)(21,22)(26,30)(27,31)(28,29);(10,14)(13,15)(17,22)(18,25)(20,28)(27,30);(8,9)(10,13)(11,12)(14,15)(16,18)(17,19)(20,26)(21,25)(22,24)(23,27)(28,31)(29,30);(16,19)(17,18)(20,27)(21,24)(22,25)(23,26)(28,30)(29,31);(8,10)(9,13)(11,14)(12,15)(16,20,21,28)(17,23,22,29)(18,26,25,31)(19,27,24,30);(8,9)(10,13)(11,12)(14,15)(16,19)(17,18)(20,27)(21,24)(22,25)(23,26)(28,30)(29,31)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55808);