Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#103 ⋊ C2 |
| Sylow | C5 ⋊ #416 |
158 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,4,5,3)(6,7,8,9)(10,13,14,12,15,21,23,22)(11,17,18,20,19,24,25,16);(10,12,15,22)(11,16,19,20)(13,23,21,14)(17,18,24,25);(2,3)(4,5)(10,11)(12,20)(13,17)(14,18)(15,19)(16,22)(21,24)(23,25)Polycyclic presentation:
2^6,5|b^2=f,c^2=d,d^2=f,e^2=f,b^a=bf,g^a=g^4,c^b=ce,d^b=df,e^b=ef56 conjugacy classes — view the full character table.
| maximal subgroup of | #10603987, #10603988, #10603991, … |
| maximal normal subgroup of | #10603987, #10603988, #10603991, … |
| maximal quotient of | #10599022, #10599026, #10599030, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 431);