Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2215 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#2253 |
| 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 | |
116 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)(8,9,11,13)(10,14,15,12)(16,17,19,22)(18,26,28,40)(20,33,31,46)(21,34,32,25)(23,37,35,29)(24,39,36,27)(30,45,44,42)(38,43,41,47);(8,10,11,15)(9,12,13,14)(17,22)(23,35)(24,36)(25,34)(26,40)(33,46)(38,41)(42,45);(16,18,27,43,21,30,31,37,19,28,39,47,32,44,20,29)(17,23,33,42,25,38,36,40,22,35,46,45,34,41,24,26)266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5488);