Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3264 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#3387 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C7 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C4×C7×Q8 ◁ G | |
326 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)(8,9,12,11)(10,14,15,13)(16,17,20,23)(18,24,25,31)(19,27,29,22)(21,28,30,26);(8,10,12,15)(9,13,11,14)(18,25)(21,30)(24,31)(26,28);(16,18,20,25)(17,21,23,30)(19,28,29,26)(22,31,27,24);(8,11,12,9)(10,13,15,14)203 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 17462);