Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#33702 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C7 |
| prime radical | C7×#3155 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C7×#117 ◁ C7×#405 ◁ G | |
602 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)(11,12)(14,15)(17,23)(18,28)(19,20)(21,32)(25,36)(26,37)(27,41)(29,30)(31,43)(33,34)(35,39)(40,46)(42,44)(45,47);(9,12)(13,15)(16,17,20,26,21,27,33,36,22,25,34,41,32,37,19,23)(18,24,28,39,30,40,42,45,31,38,43,47,44,46,29,35);(8,10,11,14)(9,13,12,15)(16,18,19,29,32,44,34,43,22,31,33,42,21,30,20,28)(17,24,23,35,37,46,41,47,25,38,36,45,27,40,26,39);(17,25)(23,36)(24,38)(26,41)(27,37)(35,45)(39,47)(40,46)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 26690);