Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1595 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#9040 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | #120 |
| commutator | C22×C4 | C22×C4×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| prime radical | C24×C7 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C23×C4×C7 ◁ G | |
750 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7)(9,11)(12,13)(14,18,19,16)(15,17)(20,21,24,28,26,29,25,34)(22,30,31,35,23,32,33,27);(8,9,10,11)(12,13)(14,16)(15,17)(18,19)(20,22,26,23)(21,27,29,35)(24,33,25,31)(28,32,34,30);(12,14)(13,16)(15,19)(17,18)(20,23,26,22)(21,27,29,35)(24,33,25,31)(28,30,34,32)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2028);