Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C7×#62773 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| socle | C22×C7 | C26 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ G | |
7998 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 6 generators on 23 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,12)(14,15)(16,17)(18,22)(19,21)(20,23);(9,12)(13,15);(16,18)(17,20)(19,23)(21,22);(18,23)(20,22);(17,21)(20,22);(8,10,11,14)(9,13,12,15)616 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55761);