Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×Q8×C241 ⋊ C2 |
| Sylow | C241 ⋊ #536 |
270 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7712 |
Polycyclic presentation:
2^6,241|b^2=e,c^2=e,b^a=be,c^a=cf,d^a=de,g^a=g^240,c^b=ce2422 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44507964, #44507980, #44507982, … |
| maximal normal subgroup of | #44507964, #44507980, #44507982, … |
| maximal quotient of | #44510031, #44510038, #44510069 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 1123);