Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3068 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#20675 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | C2×#121 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | C2×#380 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G | |
1308 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)(10,19)(11,24,26,31)(12,27)(13,17)(14,18)(15,22)(16,25,32,28)(20,29,35,39)(21,34)(23,30)(33,36,38,37);(8,10,12,22,14,21,13,23)(9,15,17,19,18,30,27,34)(11,20,25,36,26,35,28,37)(16,29,31,33,32,39,24,38);(8,11)(9,16)(10,20)(12,25)(13,28)(14,26)(15,29)(17,31)(18,32)(19,33)(21,35)(22,36)(23,37)(24,27)(30,39)(34,38);(10,21)(15,30)(19,34)(20,35)(22,23)(29,39)(33,38)(36,37)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13663);