Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2081 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#23652 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | #397 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | C2×#397 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G | |
888 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)(8,9,13,18,14,19,12,17)(10,20,22,15,24,31,23,32)(11,25,27,33,28,34,29,16)(21,36,38,39,26,30,37,35);(8,10)(9,15)(11,26)(12,22)(13,23)(14,24)(16,30)(17,31)(18,20)(19,32)(21,28)(25,39)(27,38)(29,37)(33,36)(34,35);(8,11,12,27,14,28,13,29)(9,16,17,25,19,33,18,34)(10,21,23,38,24,26,22,37)(15,30,20,35,32,36,31,39);(8,12,14,13)(9,17,19,18)(10,22,24,23)(11,27,28,29)(15,31,32,20)(16,25,33,34)(21,37,26,38)(30,39,36,35)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16640);