Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#2868 |
| 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 | |
648 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3,4,5,6,7)(9,11)(13,14)(16,17,20,23)(18,22,19,21);(16,18,20,19)(17,21,23,22);(12,13,15,14);(8,9,10,11)(12,14,15,13)(16,19,20,18)(17,22,23,21)308 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 16943);