Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1828 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#20710 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | #381 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C24 | C24×C7 |
| socle | C2×C7 | C2×#381 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G | |
1276 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)(11,22)(12,16)(13,17)(15,24)(19,26,33,30)(20,31,34,27)(23,35)(25,29)(28,36)(32,37,39,38);(8,10)(9,14)(11,19)(12,20)(13,21)(15,26)(16,27)(17,18)(22,30)(23,32)(24,33)(25,34)(28,37)(29,31)(35,38)(36,39);(8,11)(9,15,17,22)(10,19)(12,23)(13,24)(14,26,18,30)(16,28,29,35)(20,32)(21,33)(25,36)(27,37,31,38)(34,39);(8,12,13,25)(9,16,17,29)(10,20,21,34)(11,23,24,36)(14,27,18,31)(15,28,22,35)(19,32,33,39)(26,37,30,38)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13698);