Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of D80 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C5×C16 ⋊ C2 |
| Sylow | C5 ⋊ #357 |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,4,5,3)(6,7,8,9)(10,11,16,22,13,17,20,23,14,18,24,25,19,21,12,15);(2,3)(4,5)(11,15)(12,16)(13,19)(17,25)(18,23)(20,24)(21,22)Polycyclic presentation:
2^6,5|b^2=cde,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^486 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D80, #10599851, #10599852, … |
| maximal normal subgroup of | C4×D80, #10599851, #10599852, … |
| maximal quotient of | #10597995, #10598017, #10598051, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 67);