Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C5×D4 ⋊ C4 |
| Sylow | C5 ⋊ #518 |
338 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 138 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 — 4 generators on 13 points:
(1,2,3,5,4)(7,11)(10,13);(8,12)(10,13);(6,8)(7,10)(9,12)(11,13);(2,3,4,5)(6,7)(8,10)(9,11)(12,13)Polycyclic presentation:
2^6,5|a^2=e,d^a=df,g^a=g^2,c^b=cf,g^e=g^444 conjugacy classes — view the full character table.
| maximal subgroup of | #10603919, #10603925, #10604461, … |
| maximal normal subgroup of | #10603919, #10603925, #10604461, … |
| maximal quotient of | #10617061, #10617062, #10617063, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1596);