Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊Q8×C241 ⋊ C2 |
| Sylow | C241 ⋊ #492 |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7712 |
Polycyclic presentation:
2^6,241|b^2=d,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^240,g^b=g^2401702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44505611, #44506517, #44506518, … |
| maximal normal subgroup of | #44505611, #44506517, #44506518, … |
| maximal quotient of | #44507033, #44507038, #44507043, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 923);