Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×#106 ⋊ C2 |
| Sylow | C5 ⋊ #360 |
58 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)(7,11,12,20)(8,15)(9,16)(13,19,21,14)(17,18);(2,3)(4,5)(6,7)(8,11)(9,19)(10,12)(13,17)(14,16)(15,21)(18,20)Polycyclic presentation:
2^6,5|b^2=c,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^4,d^b=def,e^b=ef44 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#360, #10600044, #10600045, … |
| maximal normal subgroup of | D5×#360, #10600044, #10600045, … |
| maximal quotient of | #10597956, #10597957, #10597958, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 46);