Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C241 ⋊ #451 |
148 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7712 |
Polycyclic presentation:
2^6,241|a^2=f,b^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,g^b=g^2401699 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44506402, #44506403, #44506408, … |
| maximal normal subgroup of | #44506402, #44506403, #44506408, … |
| maximal quotient of | #44506401, #44506418, #44506469, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 704);