Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7694 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | C7×#9138 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C24×C7 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C22×C42×C7 ◁ G | |
568 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)(8,9)(10,11)(13,16)(14,17)(18,19)(20,21,24,29,25,28,23,27)(22,26,32,34,31,35,30,33);(12,13,17,19,15,18,14,16)(20,22,23,32,25,31,24,30)(21,26,29,33,28,35,27,34);(9,11)(13,18)(16,19)(20,23,25,24)(21,27,28,29)(22,30,31,32)(26,33,35,34)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2126);