Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #34980 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#35018 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C22×C7×D4 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
1732 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7)(10,14)(13,15)(16,17,19,21)(18,20,22,23)(25,29)(30,31);(9,12)(13,15)(16,17)(18,20)(19,21)(22,23)(24,25)(26,30)(27,31)(28,29);(8,9)(10,13)(11,12)(14,15)(16,17)(18,20)(19,21)(22,23)(24,26,28,27)(25,30,29,31);(8,9)(10,13)(11,12)(14,15);(8,10)(9,13)(11,14)(12,15)(16,18,19,22)(17,20,21,23)(24,27,28,26)(25,31,29,30)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 28006);