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×#3557 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C7 |
| prime radical | C7×#540 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
930 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)(10,15)(11,16)(12,20)(13,14)(17,21)(18,19)(22,23)(25,29)(26,32)(27,35)(37,39);(9,14)(11,15)(17,20)(19,22)(24,25,28,29)(26,33,32,30)(27,31,35,36)(34,39,38,37);(8,10,13,16)(9,15,14,11)(12,18,21,23)(17,22,20,19)(24,25)(26,30)(27,31)(28,29)(32,33)(34,37)(35,36)(38,39);(8,11,13,15)(9,16,14,10)(12,19,21,22)(17,23,20,18)(24,26,28,32)(25,30,29,33)(27,34,35,38)(31,37,36,39);(8,12,13,21)(9,17,14,20)(10,18,16,23)(11,19,15,22)(24,27,28,35)(25,31,29,36)(26,34,32,38)(30,37,33,39)266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19275);