Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2215 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C4 |
| direct product | C7×#2254 |
| 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 | |
128 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,11,13)(10,14,15,12)(17,21)(18,25)(19,26)(22,27)(23,31)(24,30)(28,29);(8,10,11,15)(9,12,13,14);(16,17,22,31,19,23,18,21,20,24,25,29,26,28,27,30)266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5489);