Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9239 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | C7×#9242 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #386 |
| commutator | C22×C4 | C22×C4×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| prime radical | C2×C7×#121 | C22 |
| 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)(11,19,22,17)(12,18)(14,16)(15,21,23,20)(24,25)(26,29,33,36)(27,30)(28,31)(32,35,38,39)(34,37);(8,10,13,9,14,18,12,16)(11,17,20,15,22,19,21,23)(24,26,28,33)(25,29)(27,32,34,38)(30,35)(31,36)(37,39);(8,11,14,22)(9,15,16,23)(10,17,18,19)(12,21,13,20)(24,27,28,34)(25,30,31,37)(26,32,33,38)(29,35,36,39)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2230);