Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#23425 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C7×#117 ◁ G | |
1938 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)(18,28,30,39)(19,33,36,40)(20,26,21,25)(23,32,38,31)(24,34,41,35)(29,43,44,37)(42,45,47,46);(9,11)(12,13)(14,15)(16,18)(17,23)(19,29)(20,32)(21,31)(22,30)(24,37)(25,39)(26,28)(27,38)(33,47)(34,46)(35,45)(36,44)(40,42)(41,43);(13,15)(16,19,22,36)(17,24,27,41)(18,29,30,44)(20,35,21,34)(23,37,38,43)(25,33,26,40)(28,42,39,47)(31,46,32,45);(18,30)(23,38)(28,39)(29,44)(31,32)(37,43)(42,47)(45,46)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16413);