Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#61204 |
| 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 | |
2032 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)(16,17,20,25)(18,24,28,22)(19,30,31,41)(21,34,33,26)(23,35,39,32)(27,42,43,47)(29,37,45,40)(36,44,38,46);(8,10)(9,12)(11,15)(13,14)(16,18,20,28)(17,22,25,24)(19,27,31,43)(21,29,33,45)(23,36,39,38)(26,37,34,40)(30,47,41,42)(32,44,35,46);(16,19,20,31)(17,23,25,39)(18,27,28,43)(21,35,33,32)(22,36,24,38)(26,41,34,30)(29,46,45,44)(37,42,40,47);(10,15)(12,14)(16,18)(17,24)(19,27)(20,28)(21,29)(22,25)(23,38)(26,40)(30,42)(31,43)(32,44)(33,45)(34,37)(35,46)(36,39)(41,47);(18,28)(22,24)(27,43)(29,45)(36,38)(37,40)(42,47)(44,46)385 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54192);