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 ⋊ #451 |
148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 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)(11,16)(12,18)(14,21)(15,22)(19,20)(23,25);(10,12,13,19)(11,15,16,23)(14,18,21,20)(17,25,24,22);(2,3)(4,5)(7,9)(10,11)(12,15)(13,16)(14,17)(18,25)(19,23)(20,22)(21,24)Polycyclic presentation:
2^6,5|b^2=f,c^2=df,e^2=f,c^a=cd,g^a=g^4,c^b=ce,e^b=ef,e^c=ef47 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65097, #10610526, #10610537, … |
| maximal normal subgroup of | C2×#65097, #10610526, #10610537, … |
| maximal quotient of | #10599039, #10599060, #10599061, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 435);