Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23995 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23995 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | #535 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | #2404 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C22×C4×C7 ◁ G | |
1164 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)(12,17)(13,18)(16,20)(19,30)(21,28)(22,39)(23,31)(24,32)(25,34)(26,35)(27,36)(29,38)(33,37);(8,10)(9,14)(11,22,23,38)(12,21)(13,20)(15,29,31,39)(16,18)(17,28)(19,24,36,25)(26,37)(27,32,30,34)(33,35);(8,11)(9,15)(10,19)(12,25)(13,23)(14,27)(16,30)(17,34)(18,31)(20,36)(21,38)(22,37)(24,26)(28,39)(29,33)(32,35);(8,10)(9,16)(11,19)(12,21)(13,20)(14,18)(15,30)(17,33)(22,24)(23,36)(25,38)(26,37)(27,31)(28,35)(29,34)(32,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16983);