Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2069 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#23622 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | #396 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | C2×#396 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G | |
960 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)(8,9,14,18,13,19,12,17)(10,20,28,31,23,30,22,15)(11,16,25,32,27,33,26,34)(21,35,36,29,24,38,37,39);(8,10,12,22,13,23,14,28)(9,15,18,20,19,31,17,30)(11,24,26,36,27,21,25,37)(16,29,32,38,33,39,34,35);(8,11)(9,16)(10,21)(12,25)(13,27)(14,26)(15,29)(17,32)(18,34)(19,33)(20,35)(22,36)(23,24)(28,37)(30,38)(31,39);(8,12,13,14)(9,17,19,18)(10,22,23,28)(11,25,27,26)(15,30,31,20)(16,32,33,34)(21,36,24,37)(29,38,39,35)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16610);