Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C241 ⋊ #356 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3856 |
Polycyclic presentation:
2^6,241|a^2=d,b^2=f,c^2=f,d^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^240,c^b=cf,d^b=def,d^c=df1693 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44505599, #44505600, #44505611, … |
| maximal normal subgroup of | #44505599, #44505600, #44505611, … |
| maximal quotient of | #44505379, #44505391, #44505451, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 348);