Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#102 ⋊ C2 |
| Sylow | C5 ⋊ #463 |
124 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 39 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)(7,9)(10,11)(12,15)(13,16)(14,17);(6,7,8,9)(11,15)(12,17)(14,16);(2,3)(4,5)(11,14)(12,17)(15,16)Polycyclic presentation:
2^6,5|b^2=d,e^2=f,c^a=cde,e^a=ef,g^a=g^4,c^b=cef,e^b=ef,e^c=ef47 conjugacy classes — view the full character table.
| maximal subgroup of | #10610491, #10610492, C2×#65076, … |
| maximal normal subgroup of | #10610491, #10610492, C2×#65076, … |
| maximal quotient of | #10599189, #10599190, #10599193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 414);