Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | C7×#11411 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7×C8 | C23 |
| commutator | C22 | C2×C4×C7×C8 |
| Frattini, cosocle | C4×C8 | C23×C7 |
| socle | C22×C7 | C2×C4×C8 |
| prime radical | C23×C7 | C4×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C4×C7×C8 ◁ G | |
290 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,11,14,12,15,18,21)(10,13,17,20,16,19,22,23)(25,29)(30,35)(31,36)(37,39);(8,10)(9,13)(11,17)(12,16)(14,20)(15,19)(18,22)(21,23)(24,25,26,30,27,31,32,37,28,29,33,35,34,36,38,39);(10,16)(13,19)(17,22)(20,23)784 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 4399);