Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#23833 |
| subgroup | G/H | |
|---|---|---|
| center | C7×C8 | #124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | #2398 |
| prime radical | C7×#575 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C7×C8 ◁ C22×C7×C8 ◁ G | |
616 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,19,22,32)(11,16)(12,17)(13,27)(14,18)(15,23,29,20)(21,33,35,39)(24,30)(25,37)(26,31)(28,36,38,34);(10,20,22,23)(15,19,29,32)(21,34,35,36)(28,33,38,39);(8,10)(9,15)(11,21)(12,20)(13,23)(14,22)(16,28)(17,32)(18,29)(19,27)(24,34)(25,36)(26,35)(30,39)(31,38)(33,37);(8,11,12,24,14,26,13,25)(9,16,17,30,18,31,27,37)(10,21,20,34,22,35,23,36)(15,28,32,39,29,38,19,33)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16821);