Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2218 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C4 |
| direct product | C7×#2245 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C7 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C7 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C42×C7 ◁ C4×C7×C8 ◁ G | |
132 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,12)(14,15)(16,17,23,29)(18,25,33,44)(19,24,35,42)(20,27,37,39)(21,26,30,45)(22,38,36,28)(31,43,46,41)(32,47,34,40);(9,12)(13,15)(16,18,30,46,22,32,20,19,23,33,21,31,36,34,37,35)(17,24,39,47,28,41,26,25,29,42,27,40,38,43,45,44);(8,10,11,14)(9,13,12,15)(16,19,20,34,36,46,30,33,23,35,37,32,22,31,21,18)(17,25,26,43,38,47,39,42,29,44,45,41,28,40,27,24)182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5480);