Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3057 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#3177 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C7 |
| prime radical | C23×C7 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C7×#117 ◁ G | |
338 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,12)(14,15)(16,17,21,25)(18,22,27,35)(19,29,32,44)(20,33,30,24)(23,37,38,31)(26,39,41,47)(28,43,40,36)(34,45,46,42);(9,12)(13,15)(16,18,21,27)(17,22,25,35)(19,26,32,41)(20,28,30,40)(23,34,38,46)(24,36,33,43)(29,39,44,47)(31,42,37,45);(16,19,30,37,21,32,20,31)(17,23,33,44,25,38,24,29)(18,26,40,45,27,41,28,42)(22,34,43,47,35,46,36,39);(8,10,11,14)(9,13,12,15)(18,27)(22,35)(26,41)(28,40)(34,46)(36,43)(39,47)(42,45)224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 17252);