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×#34997 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C7×#2847 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
2378 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7)(10,14)(13,15)(16,17)(18,23)(19,20)(21,22)(26,30)(27,31);(9,12)(13,15)(17,22)(18,19)(24,25,28,29)(26,31,30,27);(8,9)(10,13)(11,12)(14,15)(16,18,21,19)(17,23,22,20)(24,26)(25,27)(28,30)(29,31);(8,9)(10,13)(11,12)(14,15)(16,19,21,18)(17,20,22,23)(24,25)(26,27)(28,29)(30,31);(8,10)(9,13)(11,14)(12,15)(16,20)(17,18)(19,22)(21,23)(24,27)(25,26)(28,31)(29,30)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 27985);