Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60771 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#60939 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#3054 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C7×#117 ◁ G | |
1758 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(16,17,21,25)(18,26,27,39)(19,23,30,37)(20,32,34,24)(22,33,35,29)(28,40,41,47)(31,44,43,38)(36,45,46,42);(8,9)(10,13)(11,12)(14,15)(18,27)(22,35)(26,39)(28,41)(29,33)(36,46)(40,47)(42,45);(9,12)(13,15)(16,18,21,27)(17,22,25,35)(19,28,30,41)(20,33,34,29)(23,36,37,46)(24,39,32,26)(31,45,43,42)(38,47,44,40);(8,10,11,14)(9,13,12,15)(16,19)(17,23)(18,28)(20,31)(21,30)(22,36)(24,38)(25,37)(26,40)(27,41)(29,42)(32,44)(33,45)(34,43)(35,46)(39,47);(19,30)(23,37)(28,41)(31,43)(36,46)(38,44)(40,47)(42,45)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53927);