Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24269 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#24786 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#2414 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C4×C7×D4 ◁ G | |
990 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)(8,9,10,11)(16,17)(18,23)(19,28)(20,30)(21,25)(22,27)(24,29)(26,31);(12,13)(14,15)(16,18,20,27,21,26,29,19)(17,22,24,23,25,28,30,31);(9,11)(13,15)(18,26)(19,27)(22,28)(23,31);(16,19,29,26,21,27,20,18)(17,23,30,22,25,31,24,28)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17774);