Finite Group DatabasebetaFinite Group Databasebeta| order | 14528 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | AGL(1,ℤ/8)×C227 ⋊ C2 |
| Sylow | C227 ⋊ #575 |
262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3632 |
Polycyclic presentation:
2^6,227|d^2=f,e^2=f,b^a=be,c^a=cf,e^a=ef,e^b=ef,g^d=g^2261265 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44409079, #44409081, #44409088, … |
| maximal normal subgroup of | #44409079, #44409081, #44409088, … |
| maximal quotient of | #44408248, #44408250, #44408321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14528, 1345);