Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7×C8 · Schur multiplier (H2) = C25 |
| direct product | C7×#2988 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C24 |
| commutator | C2 | C23×C7×C8 |
| Frattini, cosocle | C2×C4 | C24×C7 |
| socle | C22×C7 | C23×C4 |
| prime radical | C2×C7×#41 | C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ G | |
432 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(16,17,18,20,19,21,22,23);(8,9)(10,13)(11,12)(14,15);(9,12)(13,15);(8,10,11,14)(9,13,12,15)476 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 17063);