Finite Group DatabasebetaFinite Group Databasebeta| order | 14912 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊Q8×C233 ⋊ C2 |
| Sylow | C233 ⋊ #529 |
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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|b^2=f,d^2=e,b^a=be,c^a=cf,g^a=g^232,g^b=g^232,g^d=g^2321652 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44450295, #44450334, #44450347, … |
| maximal normal subgroup of | #44450295, #44450334, #44450347, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14912, 1085);