Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#2514 |
| 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 | |
372 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)(9,11)(10,14)(16,17,21,19)(18,23,22,20)(26,30)(28,31);(8,9,12,11)(10,13,14,15)(16,18)(17,20)(19,23)(21,22)(24,25,27,29)(26,31,30,28);(8,10)(9,13)(11,15)(12,14)(16,19,21,17)(18,23,22,20)(24,26,27,30)(25,28,29,31);(8,11,12,9)(10,15,14,13)(16,20,21,23)(17,22,19,18)266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 16589);