Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9331 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#9342 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #386 |
| commutator | C22×C4 | C22×C4×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| prime radical | C24×C7 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
478 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,13,17,21)(11,18,19,14)(12,15)(16,20)(22,23)(24,25,28,32,29,33,27,31)(26,34,36,30,37,38,35,39);(8,10)(9,13,15,21)(11,16)(12,17)(14,20,18,23)(19,22)(24,26)(25,30)(27,36)(28,35)(29,37)(31,38)(32,34)(33,39);(8,11,12,19)(9,14,15,18)(10,16,17,22)(13,20,21,23)(24,26)(25,30)(27,35)(28,36)(29,37)(31,34)(32,38)(33,39)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2330);