Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17603 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#17606 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3489 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C7×#41 ◁ G | |
1270 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(8,9)(10,14,15,12)(11,13)(17,22,24,28)(23,29,31,30);(8,10)(9,12)(11,15)(13,14)(16,17)(18,23)(19,22)(20,28)(21,24)(25,30)(26,31)(27,29);(16,18,21,26)(17,23,24,31)(19,27,20,25)(22,29,28,30);(16,19,21,20)(17,22,24,28)(18,25,26,27)(23,30,31,29)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 10594);