Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C4×C457 ⋊ C2 |
| Sylow | C457 ⋊ #102 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7312 |
Polycyclic presentation:
2^5,457|a^2=d,c^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 | #102×D457, C2×#28410472, #44416771, … |
| maximal normal subgroup of | #102×D457, C2×#28410472, #44416771, … |
| maximal quotient of | #44416504, #44416510, #44416520, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 66);