Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#34350 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator | C22 | C24×C4×C7 |
| Frattini, cosocle | C23 | C25×C7 |
| socle | C23×C7 | C25 |
| prime radical | C2×C7×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
2106 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2,3,4,5,6,7)(8,9,10,11)(12,13)(14,18)(15,16)(17,19)(20,21)(22,28)(23,27)(24,26)(25,29)(30,34)(31,33)(32,35);(12,13)(14,17)(15,16)(18,19)(20,22)(21,25)(23,30)(24,29)(26,28)(27,32)(31,35)(33,34);(13,16)(17,18)(22,29)(25,28)(30,35)(32,34);(12,14,15,19)(13,17,16,18)(21,26)(22,29)(27,33)(30,35);(20,23,24,31)(21,27,26,33)(22,30,29,35)(25,32,28,34)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 27338);