Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C2×C7×#1951 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | #121 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C24×C7 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C23×C4×C7 ◁ G | |
918 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2)(23,24,25,26,27,28,29);(3,4,6,5)(8,13)(9,16)(10,11)(14,21)(15,19)(17,18);(3,5,6,4)(7,8)(9,14)(10,19)(11,13)(12,15)(16,20)(17,22)(18,21);(7,9,11,16,12,18,10,17)(8,14,13,20,15,21,19,22)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14167);