Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#36677 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| socle | C23×C7 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
1930 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)(9,12)(13,15)(16,17)(18,21)(19,20)(22,23)(24,25)(26,30)(27,29)(28,31);(8,9,11,12)(10,13,14,15)(24,26,27,31)(25,28,29,30);(8,10)(9,13)(11,14)(12,15)(17,20)(21,23)(26,31)(28,30);(10,14)(13,15)(25,29)(28,30);(16,18,19,22)(17,21,20,23)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29665);