Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9307 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#9328 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #386 |
| commutator | C42 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C23×C7 | #120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
444 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)(8,9,12,16,13,17,11,15)(10,18,19,22,21,23,20,14)(24,25,28,32,29,33,27,31)(26,34,36,30,37,38,35,39);(8,10)(9,14,17,22)(11,20)(12,19)(13,21)(15,23,16,18)(24,26)(25,30)(27,36)(28,35)(29,37)(31,38)(32,34)(33,39);(8,11,13,12)(9,15,17,16)(10,19,21,20)(14,18,22,23)(24,26)(25,30)(27,35)(28,36)(29,37)(31,34)(32,38)(33,39)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2316);