Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#23834 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | C2×#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 ◁ C4×C7 ◁ C22×C7×C8 ◁ G | |
608 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)(21,33,36,38)(24,30)(25,31)(26,37)(28,35,39,34);(10,20,22,23)(11,24)(15,19,29,32)(16,30)(21,35,36,34)(25,26)(28,38,39,33)(31,37);(8,10)(9,15)(11,21)(12,20)(13,23)(14,22)(16,28)(17,32)(18,29)(19,27)(24,36)(25,34)(26,35)(30,39)(31,38)(33,37);(8,11,12,25,14,24,13,26)(9,16,17,31,18,30,27,37)(10,21,20,34,22,36,23,35)(15,28,32,38,29,39,19,33)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16822);