Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1304 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C7 · Schur multiplier (H2) = C4 |
| direct product | C7×#1307 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #95 |
| commutator | C23 | C42×C7 |
| Frattini, cosocle | C2×C42 | C22×C7 |
| prime radical | C23×C7 | C42 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 2 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,12,10,11,14,13,15)(16,17)(18,24,25,21)(19,23)(20,22)(26,30,31,28)(27,29);(8,10,13,14,11,15,12,9)(16,18,19,26,20,25,27,31)(17,21,23,28,22,24,29,30)182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 439);