Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #470 |
110 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 41 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)(7,9)(10,12,14,19)(11,15,17,24)(13,22,23,20)(16,25,21,18);(6,7)(8,9)(12,19)(15,24)(18,25)(20,22);(2,3)(4,5)(7,9)(10,11,14,17)(12,18,19,25)(13,21,23,16)(15,22,24,20)Polycyclic presentation:
2^6,5|a^2=f,c^2=f,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^4,c^b=cef,d^c=df44 conjugacy classes — view the full character table.
| maximal subgroup of | #10611888, #10611893, #10611895, … |
| maximal normal subgroup of | #10611888, #10611893, #10611895, … |
| maximal quotient of | #10600306, #10600309, #10600311, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 679);