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×#62836 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
7254 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)(18,27)(19,20)(21,29)(22,23)(24,28)(25,31)(26,30);(10,14)(13,15)(17,23)(18,28)(20,25)(26,29);(8,9)(10,13)(11,12)(14,15)(16,18)(17,24)(19,29)(20,30)(21,25)(22,28)(23,27)(26,31);(16,19)(17,25)(18,29)(20,23)(21,24)(22,31)(26,28)(27,30);(8,10,11,14)(9,13,12,15)(16,20,22,25)(17,19,23,31)(18,30,28,21)(24,29,27,26);(8,9)(10,13)(11,12)(14,15)(16,21,22,30)(17,26,23,29)(18,25,28,20)(19,24,31,27)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55824);