Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2104 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#23847 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | #401 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| socle | C2×C7 | C2×#401 |
| prime radical | C24×C7 | C24 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G | |
604 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)(10,18,21,14)(11,15,24,30)(12,16)(13,17)(19,28)(20,32,34,27)(22,26)(23,29,36,39)(25,31)(33,38)(35,37);(8,10)(9,14)(11,22,24,19)(12,20)(13,21)(15,28,30,26)(16,27)(17,18)(23,35,36,33)(25,34)(29,38,39,37)(31,32);(8,11)(9,15,17,30)(10,19)(12,23)(13,24)(14,26,18,28)(16,29,31,39)(20,33)(21,22)(25,36)(27,37,32,38)(34,35);(8,12,13,25)(9,16,17,31)(10,20,21,34)(11,23,24,36)(14,27,18,32)(15,29,30,39)(19,33,22,35)(26,37,28,38)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16835);