Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #354 |
70 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)(7,11,12,20)(9,18,19,15)(10,16)(13,21)(14,17);(2,3)(4,5)(6,7,10,12)(8,14,16,21)(9,17,19,13)(11,18,20,15)Polycyclic presentation:
2^6,5|a^2=f,b^2=c,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 | #10599924, #10599925, #10599931, … |
| maximal normal subgroup of | #10599924, #10599925, #10599931, … |
| maximal quotient of | #10597940, #10597941, #10597943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 31);