Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60460 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#60711 |
| 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 | |
1846 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)(8,9)(10,13)(11,12)(14,15)(16,17,21,25)(18,26,27,39)(19,23,31,37)(20,33,28,24)(22,34,35,30)(29,40,41,47)(32,44,42,38)(36,45,46,43);(9,12)(13,15)(18,27)(22,35)(26,39)(29,41)(30,34)(36,46)(40,47)(43,45);(16,18,28,34,21,27,20,30)(17,22,33,39,25,35,24,26)(19,29,42,45,31,41,32,43)(23,36,44,47,37,46,38,40);(8,10,11,14)(9,13,12,15)(16,19)(17,23)(18,29)(20,32)(21,31)(22,36)(24,38)(25,37)(26,40)(27,41)(28,42)(30,43)(33,44)(34,45)(35,46)(39,47);(19,31)(23,37)(29,41)(32,42)(36,46)(38,44)(40,47)(43,45)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53699);