Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23542 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C24×C7 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C7×#117 ◁ G | |
1362 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(16,17,22,27)(18,28,32,39)(19,33,35,43)(20,26,21,25)(23,31,40,30)(24,37,42,36)(29,45,46,38)(34,41,47,44);(12,13)(14,15)(16,18,22,32)(17,23,27,40)(19,34,35,47)(20,31,21,30)(24,41,42,44)(25,39,26,28)(29,36,46,37)(33,45,43,38);(9,11)(13,15)(16,19,20,36,22,35,21,37)(17,24,25,33,27,42,26,43)(18,29,30,47,32,46,31,34)(23,38,28,44,40,45,39,41);(19,35)(24,42)(29,46)(33,43)(34,47)(36,37)(38,45)(41,44)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16530);