Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1795 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#20623 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | #379 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | C2×#379 |
| prime radical | C2×C7×#585 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G | |
3644 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)(11,23,26,16)(12,17)(13,27)(14,18)(15,21)(20,34,36,33)(22,30)(24,38,25,32)(28,31)(29,35,37,39);(8,10)(9,15)(11,20)(12,21)(13,28)(14,22)(16,29)(17,30)(18,31)(19,27)(23,37)(24,35)(25,39)(26,36)(32,34)(33,38);(8,11)(9,16)(10,20)(12,24)(13,25)(14,26)(15,29)(17,32)(18,23)(19,33)(21,35)(22,36)(27,38)(28,39)(30,34)(31,37);(8,12,14,13)(9,17,18,27)(10,21,22,28)(11,24,26,25)(15,30,31,19)(16,32,23,38)(20,35,36,39)(29,34,37,33)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13611);