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×#3502 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C7 |
| prime radical | C23×C7 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
964 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,11,13)(10,14,15,12)(16,17,21,25)(18,23,19,22)(20,24,28,31)(26,30,27,29);(16,18,21,19)(17,22,25,23)(20,27,28,26)(24,30,31,29);(8,10,11,15)(9,12,13,14)(16,19,21,18)(17,23,25,22)(20,27,28,26)(24,30,31,29);(16,20,21,28)(17,24,25,31)(18,26,19,27)(22,29,23,30);(16,17)(18,22)(19,23)(20,24)(21,25)(26,29)(27,30)(28,31)308 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19220);