Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10370 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#10547 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | #124 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| socle | C22×C7 | #394 |
| prime radical | C7×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C2×C42×C7 ◁ G | |
386 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,13,15)(10,11,14,12)(16,17)(18,25)(19,27)(20,28)(21,24)(22,26)(23,30)(29,31);(8,10)(9,11)(12,15)(13,14)(16,18)(17,22)(19,23)(20,29)(21,27)(24,31)(25,28)(26,30);(9,14)(10,15)(11,12)(16,19,20,22,21,25,30,31)(17,18,23,26,24,27,28,29)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3535);