Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#23268 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle, prime radical | C23×C7 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
588 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(9,12)(13,15)(16,17)(18,21)(19,20)(22,23)(24,25,29,26,28,31,37,33)(27,30,36,32,35,38,39,34);(8,9)(10,13)(11,12)(14,15)(24,26,29,31,28,33,37,25)(27,34,36,30,35,32,39,38);(8,10,11,14)(9,13,12,15)(17,20)(21,23)(24,27,28,35)(25,30,31,38)(26,32,33,34)(29,36,37,39);(9,12)(13,15)(16,18,19,22)(17,21,20,23)(25,31)(26,33)(27,35)(36,39)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16256);