Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C8 · Schur multiplier (H2) = C22 |
| direct product | C7×#7170 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C22⋊C4 |
| commutator | C2×C4 | C4×C7×C8 |
| Frattini, cosocle | C2×C4×C8 | C22×C7 |
| socle, prime radical | C23×C7 | C22⋊C8 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ C2×C4×C7×C8 ◁ G | |
262 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(13,17)(14,15)(18,19)(20,21,24,27,26,29,34,22,23,28,33,32,35,30,25,31);(9,11)(12,13,15,18,16,19,14,17)(20,22,25,30,35,27,33,28,23,31,34,29,26,32,24,21)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 158);