Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#16814532 |
| Sylow | C457 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14624 |
Polycyclic presentation:
2^5,457|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^4563668 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊#16814532, #44416506, Q8⋊#16814532, … |
| maximal normal subgroup of | D4⋊#16814532, #44416506, Q8⋊#16814532, … |
| maximal quotient of | #44416528, #44416530, #44416532, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 76);