Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10603 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#10608 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #396 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C23×C7 | C22⋊Q8 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
322 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,12,13,11,15,10,14)(16,17,22,25)(18,20,24,21)(19,26,29,30)(23,27,31,28);(16,18,20,25,22,24,21,17)(19,26,27,23,29,30,28,31);(9,13)(10,12)(14,15)(16,19,22,29)(17,23,25,31)(18,26,24,30)(20,28,21,27)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3596);