Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #356 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,5,3)(6,8,9,15,11,17,7,12)(10,16,13,14,19,20,18,21);(2,3)(4,5)(6,7,11,9)(8,14,17,21)(10,18,19,13)(12,20,15,16)Polycyclic presentation:
2^6,5|a^2=f,b^2=c,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^4,d^b=def,e^b=ef,d^c=df35 conjugacy classes — view the full character table.
| maximal subgroup of | #10599954, #10599955, #10599957, … |
| maximal normal subgroup of | #10599954, #10599955, #10599957, … |
| maximal quotient of | #10597944, #10597946, #10597948, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 36);