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×#2511 |
| 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 | |
388 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)(17,20)(18,22)(24,25,28,31)(26,30,27,29);(8,9,12,11)(10,15,14,13)(16,17)(18,21)(19,20)(22,23)(24,26,28,27)(25,29,31,30);(8,10,12,14)(9,13,11,15)(24,26,28,27)(25,29,31,30);(8,11,12,9)(10,15,14,13)(16,18,19,22)(17,21,20,23)(24,27,28,26)(25,30,31,29)266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 16586);