Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10218 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#10224 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C23×C7 | #127 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
462 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)(8,9,14,18)(10,19,11,22)(12,17,13,16)(15,21,23,20)(26,33)(27,28)(30,34)(31,37)(35,36)(38,39);(8,10,14,11)(9,15,18,23)(12,21,13,20)(16,22,17,19)(24,25)(26,34)(27,31)(28,37)(29,32)(30,36)(33,38)(35,39);(8,11,14,10)(9,15,18,23)(12,20,13,21)(16,22,17,19)(24,26)(25,30)(27,36)(28,33)(29,35)(31,39)(32,38)(34,37)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3212);