Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24390 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#29440 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C22×C7×D4 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C7×#376 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,13)(12,15)(24,25,29,31,28,33,27,32)(26,30,36,37,34,38,35,39);(8,10,11,15)(9,12,13,14)(16,17)(18,21)(19,20)(22,23)(24,26)(25,30)(27,35)(28,34)(29,36)(31,37)(32,39)(33,38);(17,20)(21,23)(25,31)(27,29)(30,37)(32,33)(35,36)(38,39);(9,13)(12,14)(16,18,19,22)(17,21,20,23)(26,34)(30,38)(35,36)(37,39)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 22428);