Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C5×C4⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ #388 |
190 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 69 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)(14,15)(16,17);(11,13)(14,15,16,17);(2,3)(4,5)(10,11)(12,13)(15,17)Polycyclic presentation:
2^6,5|b^2=f,c^2=d,b^a=be,c^a=cf,g^a=g^4,c^b=cf68 conjugacy classes — view the full character table.
| maximal subgroup of | #10605351, C4×#4044, #10605359, … |
| maximal normal subgroup of | #10605351, C4×#4044, #10605359, … |
| maximal quotient of | #10600196, #10600201, #10600210, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 617);