Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#61224 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C7×#532 ◁ G | |
2020 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)(8,9,11,13)(10,14,15,12)(16,17,21,27)(18,25,31,23)(19,32,35,43)(20,28,22,26)(24,37,41,34)(29,44,33,47)(30,39,36,42)(38,46,40,45);(8,10)(9,12)(11,15)(13,14)(16,18,21,31)(17,23,27,25)(19,33,35,29)(20,36,22,30)(24,40,41,38)(26,42,28,39)(32,44,43,47)(34,45,37,46);(16,19,21,35)(17,24,27,41)(18,29,31,33)(20,34,22,37)(23,38,25,40)(26,32,28,43)(30,45,36,46)(39,44,42,47);(10,15)(12,14)(16,18)(17,25)(19,29)(20,36)(21,31)(22,30)(23,27)(24,40)(26,39)(28,42)(32,44)(33,35)(34,46)(37,45)(38,41)(43,47);(16,20,21,22)(17,26,27,28)(18,30,31,36)(19,34,35,37)(23,39,25,42)(24,32,41,43)(29,45,33,46)(38,44,40,47)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54212);