Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×M16×C241 ⋊ C2 |
| Sylow | C241 ⋊ #568 |
258 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3856 |
Polycyclic presentation:
2^6,241|a^2=e,e^2=f,d^a=df,c^b=cf,g^c=g^2402434 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44507663, #44507666, #44507682, … |
| maximal normal subgroup of | #44507663, #44507666, #44507682, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 1315);