Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#102 ⋊ C2 |
| Sylow | C5 ⋊ #417 |
162 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,4,5,3)(6,7,8,9)(11,15)(12,17)(14,16);(10,11)(12,15)(13,14)(16,17);(2,3)(4,5)(11,14)(15,16)Polycyclic presentation:
2^6,5|c^2=d,e^2=f,b^a=bf,g^a=g^4,c^b=ce,e^b=ef,e^c=ef50 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65060, #10610473, #10610492, … |
| maximal normal subgroup of | C2×#65060, #10610473, #10610492, … |
| maximal quotient of | #10598959, #10598963, #10598967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 398);