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×#3567 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
950 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)(9,13)(10,16)(15,20)(17,22)(24,25)(26,29)(27,32)(28,33)(30,34)(31,36)(35,37)(38,39);(9,13)(14,19)(15,20)(21,23)(25,26)(27,34)(31,33)(35,39);(8,9)(10,14)(11,15)(12,13)(16,19)(17,21)(18,20)(22,23)(24,26,29,25)(27,32,34,30)(28,33,36,31)(35,38,39,37);(8,10,12,16)(9,14,13,19)(11,17,18,22)(15,21,20,23)(24,27)(25,30)(26,32)(28,35)(29,34)(31,37)(33,38)(36,39);(8,11,12,18)(9,15,13,20)(10,17,16,22)(14,21,19,23)(24,28)(25,31)(26,33)(27,35)(29,36)(30,37)(32,38)(34,39)266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19285);