Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C457 ⋊ C2 |
| Sylow | C457 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3656 |
Polycyclic presentation:
2^5,457|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^456,d^b=de,f^c=f^4561607 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,ℤ/8)×D457, C2×#28410579, #44417574, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×D457, C2×#28410579, #44417574, … |
| maximal quotient of | #44416777, #44416780, #44416816, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 173);