Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C241 ⋊ #330 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15424 |
Polycyclic presentation:
2^6,241|a^2=d,b^2=e,c^2=f,d^2=e,b^a=bc,c^a=ce,c^b=cf,d^b=def,g^b=g^2402419 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #330×D241, C2×#29507458, #44506030, … |
| maximal normal subgroup of | #330×D241, C2×#29507458, #44506030, … |
| maximal quotient of | #44505267, #44505269, #44505327, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 290);