Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28×C4 |
| direct product | C22×C7×#495 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C7 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C23×C7×D8 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ C22×C42×C7 ◁ G | |
3518 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2)(25,26,27,28,29,30,31);(3,4);(6,8)(9,10)(11,17)(12,20)(13,15)(14,18)(16,21)(19,23)(22,24);(9,11,12,18,13,19,21,24)(10,14,16,17,15,22,20,23);(5,6,7,8)(10,15)(14,22)(16,20)(17,23)616 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53619);