Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#26192 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#135 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
734 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,15)(12,14)(16,17)(18,28)(19,34)(20,37)(21,27)(22,26)(23,31)(24,36)(25,35)(29,42)(30,40)(32,44)(33,41)(38,43)(39,47)(45,46);(8,10,12,11)(9,13,14,15)(16,18,21,32)(17,23,27,41)(19,30,36,47)(20,33,22,31)(24,42,34,45)(25,40,43,39)(26,44,37,28)(29,38,46,35);(8,11,12,10)(9,13,14,15)(16,19)(17,24)(18,29)(20,35)(21,36)(22,38)(23,39)(25,26)(27,34)(28,45)(30,31)(32,46)(33,47)(37,43)(40,41)(42,44);(16,19)(17,25)(18,30)(20,38)(21,36)(22,35)(23,40)(24,26)(27,43)(28,45)(29,31)(32,47)(33,46)(34,37)(39,41)(42,44)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 19180);