Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C2×C42 |
| direct product | C7×#2844 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C7 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
356 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,11,13)(10,12,14,15)(16,17,20,19)(18,21,22,23);(10,14)(12,15)(17,19)(21,23)(24,25,27,29)(26,30,31,28);(8,9)(10,12)(11,13)(14,15)(16,18)(17,21)(19,23)(20,22)(24,26,27,31)(25,28,29,30);(8,10)(9,12)(11,14)(13,15)(16,19,20,17)(18,21,22,23)182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 16919);