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×#3556 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C7 |
| prime radical | C23×C7 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
890 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)(8,9,13,11)(10,16,18,14)(12,19,20,15)(17,21,23,22)(24,25,29,33)(26,31,27,30)(28,36,37,32)(34,38,35,39);(8,10,13,18)(9,14,11,16)(12,17,20,23)(15,21,19,22)(24,25)(26,31)(27,30)(28,32)(29,33)(34,39)(35,38)(36,37);(24,26,29,27)(25,30,33,31)(28,34,37,35)(32,38,36,39);(8,11,13,9)(10,14,18,16)(12,19,20,15)(17,21,23,22)(24,27,29,26)(25,31,33,30)(28,35,37,34)(32,39,36,38);(8,12,13,20)(9,15,11,19)(10,17,18,23)(14,21,16,22)(24,28,29,37)(25,32,33,36)(26,34,27,35)(30,38,31,39)266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19274);