Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#22105 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C23×C7 | C23×C4 |
| prime radical | C24×C7 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
708 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(13,16)(14,18)(20,21,26,22,25,29,24,28)(23,27,31,30,32,34,33,35);(12,13)(14,17)(15,16)(18,19)(20,22,26,29,25,28,24,21)(23,30,31,34,32,35,33,27);(9,11)(13,16)(17,19)(20,23)(21,27)(22,30)(24,33)(25,32)(26,31)(28,35)(29,34);(12,14,15,18)(13,17,16,19)(20,24,25,26)(21,28,29,22)(23,31,32,33)(27,30,34,35)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 15093);