Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#2776 |
| 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 | |
344 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)(10,13)(11,12)(14,15)(16,17,20,21)(18,22,23,19)(24,25,28,31)(26,29,30,27);(9,11)(10,14)(17,21)(19,22)(24,26,28,30)(25,29,31,27);(8,10,12,14)(9,13,11,15)(16,18,20,23)(17,22,21,19)(24,27,28,29)(25,30,31,26);(8,11,12,9)(10,15,14,13)(16,19,20,22)(17,23,21,18)(24,25)(26,29)(27,30)(28,31)224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 16851);