Finite Group DatabasebetaFinite Group Databasebeta| order | 14528 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×SD16×C227 ⋊ C2 |
| Sylow | C227 ⋊ #448 |
158 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7264 |
Polycyclic presentation:
2^6,227|b^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,g^c=g^2261601 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #448×D227, C2×#28409169, #44408948, … |
| maximal normal subgroup of | #448×D227, C2×#28409169, #44408948, … |
| maximal quotient of | #44398655, #44398672, #44398723, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14528, 686);