Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18618 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18651 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3499 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
1126 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,12,15)(10,14,11,13)(17,22)(18,26)(19,20)(24,25)(27,28)(29,30);(9,13)(10,11)(14,15)(16,17,21,25)(18,23,27,31)(19,22,20,24)(26,29,28,30);(16,18)(17,23)(19,26)(20,28)(21,27)(22,29)(24,30)(25,31);(8,10,12,11)(9,13,15,14)(16,19,21,20)(17,24,25,22)(18,26,27,28)(23,30,31,29)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11639);