Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊Q8×C241 ⋊ C2 |
| Sylow | C241 ⋊ #461 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7712 |
Polycyclic presentation:
2^6,241|a^2=f,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,e^c=ef,g^c=g^2401699 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44506621, #44506623, #44506642, … |
| maximal normal subgroup of | #44506621, #44506623, #44506642, … |
| maximal quotient of | #44506817, #44506831, #44506841, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 751);