Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23996 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23997 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2404 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| prime radical | C7×#3026 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C24×C7 ◁ G | |
1210 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)(10,14)(11,15)(12,16)(13,17)(18,25)(19,26)(20,27)(21,33)(22,35)(23,29)(24,30)(28,36)(31,39)(32,38)(34,37);(8,10,13,20)(9,14,17,27)(11,21)(12,19,24,32)(15,25)(16,26,30,38)(18,23)(22,34)(28,37)(29,33)(31,36)(35,39);(8,11)(9,15)(10,18)(12,22)(13,23)(14,25)(16,28)(17,29)(19,31)(20,21)(24,36)(26,37)(27,33)(30,35)(32,34)(38,39);(8,12)(9,16)(10,19)(11,22)(13,24)(14,26)(15,28)(17,30)(18,31)(20,32)(21,34)(23,36)(25,37)(27,38)(29,35)(33,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16985);