Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C5×#124 ⋊ C2 |
| Sylow | C5 ⋊ #495 |
130 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 43 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)(11,16)(12,20)(13,22)(15,23)(17,18)(19,24);(6,7,8,9)(10,12)(11,15)(13,21)(14,20)(16,24)(17,23)(18,19)(22,25);(2,3)(4,5)(7,9)(10,11)(12,19)(13,16)(14,18)(15,20)(17,22)(21,23)(24,25)Polycyclic presentation:
2^6,5|b^2=ef,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^4,c^b=ce,d^c=df50 conjugacy classes — view the full character table.
| maximal subgroup of | #10612020, #10612027, #10612255, … |
| maximal normal subgroup of | #10612020, #10612027, #10612255, … |
| maximal quotient of | #10600342, #10600344, #10600351, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 686);