Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18284 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18312 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3455 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
930 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(9,13)(10,11)(14,15)(16,17,21,25)(18,22,28,35)(19,23,30,37)(20,31,32,24)(26,38,40,33)(27,41,42,34)(29,43,44,36)(39,45,47,46);(8,9)(10,13)(11,15)(12,14)(16,18)(17,22)(19,26)(20,27)(21,28)(23,33)(24,34)(25,35)(29,39)(30,40)(31,41)(32,42)(36,45)(37,38)(43,46)(44,47);(8,10,12,11)(9,13,14,15)(16,19)(17,23)(18,26)(20,29)(21,30)(22,33)(24,36)(25,37)(27,39)(28,40)(31,43)(32,44)(34,45)(35,38)(41,46)(42,47);(16,20,21,32)(17,24,25,31)(18,27,28,42)(19,29,30,44)(22,34,35,41)(23,36,37,43)(26,39,40,47)(33,45,38,46)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11300);