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×#3564 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C7 |
| prime radical | C7×#538 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
936 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,13,17)(10,18,19,15)(11,22,25,16)(12,14,24,28)(20,30,32,31)(21,29,33,26)(23,36,37,27)(34,39,35,38);(9,14)(10,19)(11,23)(15,29)(17,28)(18,26)(20,34)(21,33)(25,37)(30,31)(32,35)(38,39);(8,10,12,21)(9,15,14,26)(11,20,23,35)(13,19,24,33)(16,30,27,38)(17,18,28,29)(22,31,36,39)(25,32,37,34);(8,11,24,37)(9,16,28,36)(10,20,33,34)(12,23,13,25)(14,27,17,22)(15,30,29,39)(18,31,26,38)(19,32,21,35);(9,14)(15,26)(16,27)(17,28)(18,29)(22,36)(30,38)(31,39)266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19282);