Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of D80 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #367 |
46 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,4,5,3)(10,11,16,22,21,25,12,15,14,18,19,24,13,17,20,23);(2,3)(4,5)(6,7,8,9)(11,15)(12,19)(13,21)(16,20)(17,24)(18,23)(22,25)Polycyclic presentation:
2^6,5|a^2=c,b^2=de,d^2=e,e^2=f,b^a=bd,d^a=def,e^a=ef,g^a=g^486 conjugacy classes — view the full character table.
| maximal subgroup of | #10598073, #10598092, #10598097, … |
| maximal normal subgroup of | #10598073, #10598092, #10598097, … |
| maximal quotient of | #10597992, #10598092, #10598297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 63);