Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18746 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18760 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
932 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)(9,13)(10,11)(14,15)(16,17)(18,27)(19,30)(20,26)(21,25)(22,24)(23,28)(29,31);(8,9)(10,13)(11,15)(12,14)(16,18,22,19)(17,23,24,31)(20,29,21,28)(25,30,26,27);(8,10,12,11)(9,13,14,15)(16,19,22,18)(17,23,24,31)(20,28,21,29)(25,30,26,27);(17,24)(23,31)(25,26)(27,30)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11748);