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) = C24 |
| direct product | C7×#8984 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | #120 |
| commutator | C42 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C22×C7×D4 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ G | |
592 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7)(9,11)(12,13,14,18,16,19,15,17)(20,21,24,28,25,29,23,27)(22,30,31,26,33,34,32,35);(8,9,10,11)(13,17)(14,15)(18,19)(20,22)(21,26)(23,31)(24,32)(25,33)(27,34)(28,30)(29,35);(13,18)(14,15)(17,19)(20,23,25,24)(21,27,29,28)(22,31,33,32)(26,34,35,30)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1972);