Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C239 ⋊ C2 |
| Sylow | C239 ⋊ #509 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3824 |
Polycyclic presentation:
2^6,239|d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^238,d^b=de,e^b=ef,g^b=g^2382396 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44486445, #44486448, #44486495, … |
| maximal normal subgroup of | #44486445, #44486448, #44486495, … |
| maximal quotient of | #44486261, #44486265, #44486336, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 987);