Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C5×#97 ⋊ C2 |
| Sylow | C5 ⋊ #489 |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(7,11)(10,12)(14,16,20,15,18,21,17,19);(6,8,9,13)(7,10,11,12)(15,19)(16,21);(2,3)(4,5)(6,7)(8,12)(9,11)(10,13)(14,15)(16,20)(17,21)(18,19)Polycyclic presentation:
2^6,5|b^2=ef,c^2=de,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^4,c^b=cf56 conjugacy classes — view the full character table.
| maximal subgroup of | #10599145, #10599146, #10599149, … |
| maximal normal subgroup of | #10599145, #10599146, #10599149, … |
| maximal quotient of | #10599423, #10599428, #10599429, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 341);