Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×C22⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ #385 |
234 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 64 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) = 40 |
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);(2,3,4,5)(11,13)Polycyclic presentation:
2^6,5|a^2=d,c^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 | #10603919, C2×#65699, #10617071, … |
| maximal normal subgroup of | #10603919, C2×#65699, #10617071, … |
| maximal quotient of | #10603785, #10603786, #10603787, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1037);