Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3264 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#18089 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C22×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C42 | C24×C7 |
| socle | C22×C7 | C2×C4×D4 |
| prime radical | C7×#532 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C7×#431 ◁ G | |
604 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,17)(11,13)(12,15)(14,18)(16,20)(19,22)(21,23)(24,25,28,32,29,26,33,31)(27,34,35,38,36,30,37,39);(9,13)(11,20)(14,21)(15,16)(17,22)(19,23)(24,26)(25,29)(27,34)(28,31)(30,36)(32,33)(35,38)(37,39);(8,10)(9,14)(11,19)(12,18)(13,21)(15,17)(16,22)(20,23)(24,27,28,35,29,36,33,37)(25,30,32,39,26,34,31,38);(9,15)(10,18)(13,16)(19,23)(25,26)(30,34)(31,32)(38,39)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11077);