Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#3555 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C7 |
| prime radical | C7×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
910 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,13,16)(10,11,18,14)(12,20,21,15)(17,22,23,19)(24,25,28,31)(26,29,34,32)(27,35,36,30)(33,38,39,37);(8,10,13,18)(9,14,16,11)(12,17,21,23)(15,22,20,19)(24,25)(26,32)(27,30)(28,31)(29,34)(33,38)(35,36)(37,39);(8,11,13,14)(9,10,16,18)(12,19,21,22)(15,17,20,23);(8,10)(9,14)(11,16)(12,17)(13,18)(15,22)(19,20)(21,23)(24,26)(25,29)(27,33)(28,34)(30,37)(31,32)(35,38)(36,39);(8,12,13,21)(9,15,16,20)(10,17,18,23)(11,19,14,22)(24,27,28,36)(25,30,31,35)(26,33,34,39)(29,37,32,38)266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19273);