Finite Group DatabasebetaFinite Group Databasebeta| order | 14528 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #104×C227 ⋊ C2 |
| Sylow | C227 ⋊ #453 |
168 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 168 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.
| transitive degree | μt(G) = 1816 |
Polycyclic presentation:
2^6,227|d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^226,d^b=df,e^b=ef,d^c=df,g^c=g^2261598 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #453×D227, C2×#28409201, #44409085, … |
| maximal normal subgroup of | #453×D227, C2×#28409201, #44409085, … |
| maximal quotient of | #44398653, #44398658, #44398681, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14528, 718);