Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#36701 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| socle, prime radical | C23×C7 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
1304 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,12)(14,15)(16,17)(18,22)(19,23)(20,21)(24,30)(25,28)(26,31)(27,29)(32,33,36,39)(34,37,41,45)(35,38,43,47)(40,44,42,46);(17,21)(22,28)(23,29)(30,31)(32,34,36,41)(33,37,39,45)(35,42,43,40)(38,46,47,44);(9,12)(13,15)(16,18,20,25)(17,22,21,28)(19,26,27,24)(23,31,29,30)(32,35)(33,38)(34,40)(36,43)(37,44)(39,47)(41,42)(45,46);(16,19,20,27)(17,23,21,29)(18,24,25,26)(22,30,28,31)(33,39)(35,43)(37,45)(40,42);(8,10,11,14)(9,13,12,15)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29689);