Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7943 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | C7×#7976 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#95 |
| commutator | C2×C4 | C2×C42×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C24×C7 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C42×C7 ◁ G | |
562 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)(11,15)(12,21)(13,16)(14,18)(19,22)(20,23)(24,25)(26,33,35,39)(27,31)(28,37)(29,32)(30,34,38,36);(8,10)(9,14,16,23)(11,20)(12,18)(13,19)(15,17,21,22)(24,26,28,36,29,35,27,34)(25,30,31,33,32,38,37,39);(8,11,13,12)(9,15,16,21)(10,18,19,20)(14,22,23,17)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 964);