Finite Group DatabasebetaFinite Group Databasebeta| order | 14912 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C8×C233 ⋊ C2 |
| Sylow | C233 ⋊ D4⋊C8 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7456 |
Polycyclic presentation:
2^6,233|a^2=d,c^2=e,d^2=f,b^a=bc,c^a=ce,c^b=ce,g^b=g^2322348 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊C8×D233, C2×#28416162, #44450190, … |
| maximal normal subgroup of | D4⋊C8×D233, C2×#28416162, #44450190, … |
| maximal quotient of | #44449630, #44449634, #44449649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14912, 276);