Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C8 · Schur multiplier (H2) = C2 |
| direct product | C7×#1313 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C42 |
| commutator | C4 | C4×C7×C8 |
| Frattini, cosocle | C4×C8 | C22×C7 |
| socle, prime radical | C22×C7 | #97 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ G | |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 2 generators on 31 points:
(1,2,3,4,5,6,7)(16,17,18,22,19,24,26,30,20,23,25,31,27,21,28,29);(8,9,10,12,11,13,14,15)(17,21,23,24)(18,25)(22,30,31,29)(26,28)308 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 445);