Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C5×C22⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ #388 |
190 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 13 points:
(1,2,3,5,4)(7,9)(10,11)(12,13);(6,7)(8,9)(10,11,12,13);(2,3,4,5)(10,11,12,13)Polycyclic presentation:
2^6,5|a^2=d,b^2=e,c^a=ce,g^a=g^2,c^b=cf,g^d=g^438 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65700, #10617070, #10617072, … |
| maximal normal subgroup of | C2×#65700, #10617070, #10617072, … |
| maximal quotient of | #10603792, #10603793, #10603794, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1038);