Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C457 ⋊ C22⋊Q8 |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7312 |
Polycyclic presentation:
2^5,457|a^2=d,b^2=d,b^a=bd,c^a=ce,f^b=f^4562294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊Q8×D457, C2×#28410529, #44417283, … |
| maximal normal subgroup of | C22⋊Q8×D457, C2×#28410529, #44417283, … |
| maximal quotient of | #44416635, #44416649, #44416652, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 123);