Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#103 ⋊ C2 |
| Sylow | C5 ⋊ #452 |
152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 152 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)(10,12,14,20)(11,16,15,18)(13,22,21,19)(17,24,23,25);(6,7,8,9)(11,15)(12,19)(13,21)(16,24)(18,25)(20,22);(2,3)(4,5)(7,9)(10,11)(12,18)(13,17)(14,15)(16,20)(19,24)(21,23)(22,25)Polycyclic presentation:
2^6,5|b^2=ef,c^2=f,d^2=f,b^a=be,c^a=cf,g^a=g^4,c^b=cd,d^b=df,d^c=df47 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65099, #10610526, #10610538, … |
| maximal normal subgroup of | C2×#65099, #10610526, #10610538, … |
| maximal quotient of | #10599040, #10599046, #10599053, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 437);