Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C22⋊C4×C457 ⋊ C2 |
| Sylow | C457 ⋊ #124 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7312 |
Polycyclic presentation:
2^5,457|b^2=e,c^2=d,b^a=bd,c^a=ce,f^c=f^4562294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #124×D457, C2×#28410538, #44417304, … |
| maximal normal subgroup of | #124×D457, C2×#28410538, #44417304, … |
| maximal quotient of | #44416641, #44416665, #44416666, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 132);