Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2021 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#2030 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #120 |
| commutator, Frattini, cosocle | C24 | C23×C7 |
| prime radical | C24×C7 | C23 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C24×C7 ◁ G | |
290 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 224 |
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)(16,17)(18,21)(19,22)(20,23)(24,29)(25,28)(26,30)(27,31);(8,10,11,15)(9,12,13,14)(16,18)(17,21)(19,24)(20,25)(22,29)(23,28)(26,31)(27,30);(16,19,20,26)(17,22,23,30)(18,24,25,31)(21,27,28,29)182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5265);