Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#102 ⋊ 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)(6,7,8,9)(11,16)(12,19)(14,22)(15,23)(18,25)(20,21);(10,12)(11,15)(13,20)(14,19)(16,18)(17,25)(21,22)(23,24);(2,3)(4,5)(7,9)(10,11)(12,18)(13,16)(14,17)(15,20)(19,23)(21,25)(22,24)Polycyclic presentation:
2^6,5|c^2=df,e^2=f,b^a=bf,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×#65072, #10610478, #10610490, … |
| maximal normal subgroup of | C2×#65072, #10610478, #10610490, … |
| maximal quotient of | #10598995, #10598996, #10598997, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 410);