Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C457 ⋊ Q32 |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14624 |
Polycyclic presentation:
2^5,457|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,c^b=cd,d^b=de,f^b=f^4561607 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q32×D457, C2×#28410498, #44417207, … |
| maximal normal subgroup of | Q32×D457, C2×#28410498, #44417207, … |
| maximal quotient of | #44416580, #44416581, #44416602, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 92);