Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D4×C457 ⋊ C4 |
| 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,f^a=f^348,c^b=ce,f^d=f^456584 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#28410616, D457⋊#104, #44417774, … |
| maximal normal subgroup of | C2×#28410616, D457⋊#104, #44417774, … |
| maximal quotient of | D4⋊#16814539, #44417627, #44417628, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 210);