Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4×#120 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#36587 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C7×#2856 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
2040 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)(8,9)(10,15)(11,13)(12,14)(16,17,21,19)(18,22,20,23)(24,25)(26,28)(27,30)(29,31);(8,10)(9,13)(11,12)(14,15)(16,17,21,19)(18,23,20,22)(24,26,29,30)(25,27,31,28);(8,9,12,14)(10,15,11,13)(16,18,21,20)(17,22,19,23)(24,27,29,28)(25,30,31,26);(8,9)(10,13)(11,15)(12,14)(16,19,21,17)(18,22,20,23)(24,25)(26,27)(28,30)(29,31);(8,11,12,10)(9,13,14,15)(16,20,21,18)(17,23,19,22)(24,28,29,27)(25,26,31,30)490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29575);