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×#3509 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C7 |
| prime radical | C2×C7×#41 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
992 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)(16,17,20,23)(18,21,26,24)(19,27,28,22)(25,30,31,29);(8,9,11,13)(10,12,14,15)(16,17)(18,24)(19,22)(20,23)(21,26)(25,30)(27,28)(29,31);(8,10,11,14)(9,12,13,15);(16,18)(17,21)(19,25)(20,26)(22,29)(23,24)(27,30)(28,31);(16,19,20,28)(17,22,23,27)(18,25,26,31)(21,29,24,30)308 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19227);