Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1619 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#9060 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | #120 |
| commutator | C42 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ G | |
522 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7)(9,11)(13,16)(14,18)(17,19)(20,21,24,26,25,29,23,28)(22,30,32,27,33,34,31,35);(8,9,10,11)(21,26)(23,24)(27,30)(28,29)(31,32)(34,35);(12,13,15,17)(14,19,18,16)(20,22,25,33)(21,27,29,35)(23,32,24,31)(26,30,28,34)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2048);