Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #3958 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #358 |
58 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)(6,7,8,9)(11,15)(12,19)(13,20)(16,17)(18,24)(21,25)(22,23);(2,3)(4,5)(10,11,14,18)(12,15,21,24)(13,22,20,17)(16,25,23,19)Polycyclic presentation:
2^6,5|a^2=f,b^2=c,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^4,d^b=de,e^b=ef50 conjugacy classes — view the full character table.
| maximal subgroup of | #10599977, #10599978, #10599981, … |
| maximal normal subgroup of | #10599977, #10599978, #10599981, … |
| maximal quotient of | #10597963, #10597965, #10597967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 50);