Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C214 |
| direct product | C22×C7×#536 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C7 | C24 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| prime radical | C23×C7×#41 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
11406 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 6 generators on 31 points:
(1,2)(25,26,27,28,29,30,31);(3,4);(6,8)(10,14)(11,17)(12,20)(22,24);(9,10,13,14)(11,18,17,15)(12,16,20,21)(19,24,23,22);(5,6)(7,8)(9,11,13,17)(10,15,14,18)(12,19,20,23)(16,22,21,24);(9,12)(10,16)(11,19)(13,20)(14,21)(15,22)(17,23)(18,24)616 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55668);