Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #106×C241 ⋊ C2 |
| Sylow | C241 ⋊ #469 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7712 |
Polycyclic presentation:
2^6,241|b^2=df,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^240,c^b=cf,g^c=g^2401696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44509392, #44509661 |
| maximal normal subgroup of | #44509392, #44509661 |
| maximal quotient of | #44506925, #44506930, #44506959, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 803);