Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9415 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#9415 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #386 |
| commutator | C42 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C7×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
420 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)(10,17,18,21)(11,14,19,20)(12,15)(13,16)(22,23)(24,25)(26,29,33,38)(27,30)(28,31)(32,35)(34,36,39,37);(8,10,12,20,13,18,22,14)(9,11,15,21,16,19,23,17)(24,26)(25,29,31,38)(27,34)(28,33)(30,36,32,37)(35,39);(8,11)(9,14)(10,15)(12,21)(13,19)(16,20)(17,22)(18,23)(25,30)(27,35)(29,36)(31,32)(34,39)(37,38)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2403);