Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42×C7 · Schur multiplier (H2) = C28×C4 |
| direct product | C22×C4×C7×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C42×C7 | C22 |
| commutator | C2 | C23×C42×C7 |
| Frattini, cosocle | C2×C4 | C25×C7 |
| socle | C24×C7 | C22×C4 |
| prime radical | C25×C7 | C2×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C42×C7 ◁ G | |
3950 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 23 points:
(1,2)(17,18,19,20,21,22,23);(3,4);(5,6,7,8);(9,10,11,12,13,14,15,16);(10,14)(12,16)1120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53040);