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×#3512 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
1032 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)(18,23)(19,24)(20,28)(21,22)(25,29)(26,27)(30,31);(8,9,11,13)(10,12,14,15)(17,22)(19,23)(25,28)(27,30);(8,10,11,14)(9,12,13,15)(16,18,21,24)(17,23,22,19)(20,26,29,31)(25,30,28,27);(16,19,21,23)(17,24,22,18)(20,27,29,30)(25,31,28,26);(16,20,21,29)(17,25,22,28)(18,26,24,31)(19,27,23,30)308 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19230);