Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#3507 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C7 |
| prime radical | C7×#532 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
1012 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7)(10,14)(12,15)(16,17)(18,25)(19,20)(21,22)(23,28)(24,29)(26,31)(27,30);(8,9,11,13)(10,12,14,15)(17,22)(19,24)(23,25)(26,30);(8,10,11,14)(9,12,13,15)(16,18,21,28)(17,23,22,25)(19,26,24,30)(20,27,29,31);(16,19,21,24)(17,20,22,29)(18,26,28,30)(23,27,25,31);(16,20)(17,24)(18,27)(19,22)(21,29)(23,30)(25,26)(28,31)308 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19225);