Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#97 ⋊ C2 |
| Sylow | C5 ⋊ #444 |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(6,9,10,17,11,18,19,8)(7,12,13,20,15,21,14,16);(6,8,10,9,11,17,19,18)(7,12,14,16,15,21,13,20);(2,3)(4,5)(6,7)(8,16)(9,12)(10,13)(11,15)(14,19)(17,20)(18,21)Polycyclic presentation:
2^6,5|b^2=e,c^2=d,d^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^4,c^b=cf62 conjugacy classes — view the full character table.
| maximal subgroup of | #10599883, #10599884, #10601710, … |
| maximal normal subgroup of | #10599883, #10599884, #10601710, … |
| maximal quotient of | #10598869, #10598870, #10598871, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 344);