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×#2244 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C7 |
| prime radical | C7×#493 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C42×C7 ◁ C4×C7×C8 ◁ G | |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,12)(14,15)(17,23)(18,29)(19,24)(20,31)(21,25)(26,27)(28,30);(9,12)(13,15)(16,17,24,18,21,27,31,30,22,28,20,26,25,29,19,23);(8,10,11,14)(9,13,12,15)(16,18,19,17,25,23,20,29,22,26,31,28,21,30,24,27)182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5479);