Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#10178 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C2×C7×#459 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
592 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(13,15)(16,17)(18,25)(19,22)(20,24)(21,27)(23,29)(26,31)(28,30);(8,9,11,13)(10,15,14,12)(16,18,20,28)(17,21,24,31)(19,26,29,27)(22,25,23,30);(17,22)(18,26)(19,29)(23,24)(25,30)(27,28)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3166);