Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23464 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C24×C7 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1146 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)(8,9,11,13)(10,14,15,12)(16,17)(18,23)(19,30)(20,25)(21,34)(22,26)(24,32)(27,43)(28,37)(29,39)(31,41)(33,42)(35,38)(36,44)(40,46)(45,47);(8,10,11,15)(9,12,13,14)(16,18)(17,23)(19,27)(20,28)(21,35)(22,29)(24,40)(25,37)(26,39)(30,43)(31,44)(32,46)(33,45)(34,38)(36,41)(42,47);(16,19,22,33)(17,24,26,41)(18,27,29,45)(20,32,21,31)(23,36,39,40)(25,42,34,30)(28,46,35,44)(37,43,38,47);(16,20,22,21)(17,25,26,34)(18,28,29,35)(19,31,33,32)(23,37,39,38)(24,30,41,42)(27,44,45,46)(36,47,40,43)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16452);