Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60454 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#60699 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#3060 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C4×C7×#41 ◁ G | |
1842 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
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)(16,17,21,25)(18,22,27,35)(19,29,31,44)(20,33,30,24)(23,37,38,32)(26,39,41,47)(28,43,40,36)(34,45,46,42);(9,12)(13,15)(16,18)(17,22)(19,26)(20,28)(21,27)(23,34)(24,36)(25,35)(29,39)(30,40)(31,41)(32,42)(33,43)(37,45)(38,46)(44,47);(16,19,30,37,21,31,20,32)(17,23,33,44,25,38,24,29)(18,26,40,45,27,41,28,42)(22,34,43,47,35,46,36,39);(8,10,11,14)(9,13,12,15)(19,31)(23,38)(26,41)(29,44)(32,37)(34,46)(39,47)(42,45);(18,27)(22,35)(26,41)(28,40)(34,46)(36,43)(39,47)(42,45)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53687);