Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23848 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#23852 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#546 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C4×C7×D4 ◁ G | |
1900 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(16,17,20,24)(18,22,26,30)(19,21,27,23)(25,28,31,29);(12,13)(14,15)(17,21)(19,27)(22,28)(23,24)(25,31)(29,30);(9,11)(13,15)(16,18,20,26)(17,22,24,30)(19,25,27,31)(21,28,23,29);(17,21)(19,27)(22,28)(23,24)(25,31)(29,30)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16840);