Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C457 ⋊ #126 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7312 |
Polycyclic presentation:
2^5,457|b^2=de,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 | #126×D457, C2×#28410545, #44417304, … |
| maximal normal subgroup of | #126×D457, C2×#28410545, #44417304, … |
| maximal quotient of | #44416644, #44416659, #44416662, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 139);