Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1304 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#1308 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #95 |
| commutator | C23 | C42×C7 |
| Frattini, cosocle | C2×C42 | C22×C7 |
| prime radical | C23×C7 | C42 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 2 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,11,16,13,15,12,17)(10,18,19,23,20,14,21,22)(24,25,27,30,28,31,35,38)(26,32,34,39,33,29,36,37);(8,10,12,19,13,20,11,21)(9,14,17,22,15,18,16,23)(24,26)(25,29,31,32)(27,34)(28,33)(30,37,38,39)(35,36)182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 440);