Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M16×C457 ⋊ C2 |
| Sylow | C457 ⋊ #104 |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3656 |
Polycyclic presentation:
2^5,457|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,c^b=ce,f^b=f^4562294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #104×D457, C2×#28410478, #44416792, … |
| maximal normal subgroup of | #104×D457, C2×#28410478, #44416792, … |
| maximal quotient of | #44416504, #44416507, #44416512, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 72);