Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#102 ⋊ 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)(10,12,13,21,15,22,14,20)(11,17,18,24,16,23,19,25);(11,16)(12,20)(13,14)(17,24)(21,22)(23,25);(2,3)(4,5)(10,11)(12,17)(13,18)(14,19)(15,16)(20,25)(21,24)(22,23)Polycyclic presentation:
2^6,5|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 | #10603955, #10603956, #10603959, … |
| maximal normal subgroup of | #10603955, #10603956, #10603959, … |
| maximal quotient of | #10598958, #10598962, #10598966, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 399);