Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1828 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#1830 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #381 |
| commutator | C23 | C22×C4×C7 |
| Frattini, cosocle | C22×C4 | C23×C7 |
| prime radical | C23×C7 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
236 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,12,17,13,16,26,31)(10,18,20,32,21,14,25,28)(11,22,24,36,23,15,29,30)(19,27,35,38,34,33,37,39);(8,10,13,21)(9,14,16,18)(11,19,23,34)(12,25,26,20)(15,27,22,33)(17,32,31,28)(24,37,29,35)(30,39,36,38);(8,11)(9,15,16,22)(10,19)(12,24)(13,23)(14,27,18,33)(17,30,31,36)(20,35)(21,34)(25,37)(26,29)(28,38,32,39)203 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5065);