Finite Group DatabasebetaFinite Group Databasebeta| order | 14912 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C233 ⋊ #399 |
186 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7456 |
Polycyclic presentation:
2^6,233|a^2=d,b^2=de,b^a=bd,c^a=ce,c^b=cf,g^b=g^2322342 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44449833, #44449835, #44450830, … |
| maximal normal subgroup of | #44449833, #44449835, #44450830, … |
| maximal quotient of | #44450053, #44450055, #44450074, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14912, 485);