Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#446 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C5 | C23 |
| commutator | C22 | C22×C4×C5 |
| Frattini, cosocle | C2×C4 | C23×C5 |
| socle, prime radical | C22×C5 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C5 ◁ G | |
94 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,6)(3,7,8,5)(9,10,12,11,13,14,16,15)(17,18,19,20,21);(1,3,4,8)(2,5,6,7);(9,11,12,14,13,15,16,10)140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 947);