Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#3501 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C7 |
| prime radical | C22×C7×D4 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
1100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 5 generators on 23 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,12)(13,15)(16,17,19,21)(18,22,23,20);(9,12)(13,14);(16,18,19,23)(17,20,21,22);(8,9)(10,13)(11,12)(14,15);(8,10)(9,13)(11,15)(12,14)308 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19219);