Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | C7×#2508 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C7 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
380 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,12,10)(11,14,15,13)(17,19)(18,22)(25,29)(27,30);(9,10)(13,14)(16,17,20,19)(18,21,22,23)(24,25)(26,30)(27,31)(28,29);(8,10,12,9)(11,14,15,13)(16,18)(17,21)(19,23)(20,22)(24,26,28,31)(25,30,29,27);(8,11,12,15)(9,13,10,14)(16,19,20,17)(18,23,22,21)(24,27,28,30)(25,31,29,26)266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 16583);