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×#2824 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C7 |
| prime radical | C7×#392 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
472 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(9,12)(13,15)(16,17,19,20)(18,21,23,22)(24,25)(26,29)(27,28)(30,31);(10,14)(13,15)(17,20)(21,22)(25,28)(29,30);(8,9)(10,13)(11,12)(14,15)(16,17)(18,22)(19,20)(21,23)(24,26)(25,29)(27,31)(28,30);(8,10)(9,13)(11,14)(12,15)(16,18)(17,21)(19,23)(20,22)(24,25)(26,30)(27,28)(29,31)182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 16899);