Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4×#120 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#36590 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C22×C7×D4 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
1666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,13,11)(10,14,12,15)(17,21)(18,23)(25,29)(30,31);(8,9,13,11)(10,15,12,14)(16,17)(18,22)(19,23)(20,21)(24,25,28,29)(26,30,27,31);(8,10,13,12)(9,14,11,15)(16,18,20,23)(17,22,21,19)(24,26,28,27)(25,30,29,31);(8,11,13,9)(10,14,12,15)(16,19,20,22)(17,23,21,18)(24,27,28,26)(25,31,29,30);(8,12,13,10)(9,15,11,14)490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29578);