Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C241 ⋊ #361 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3856 |
Polycyclic presentation:
2^6,241|a^2=d,c^2=e,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^240,c^b=cef,d^b=df,e^b=ef1696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #361×D241, C2×#29507530, #44509191, … |
| maximal normal subgroup of | #361×D241, C2×#29507530, #44509191, … |
| maximal quotient of | #44505412, #44505460, #44505491, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 362);