Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C239 ⋊ #480 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|c^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,e^c=ef,g^c=g^2381685 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44483534, #44483535, #44483545, … |
| maximal normal subgroup of | #44483534, #44483535, #44483545, … |
| maximal quotient of | #44484632, #44484735, #44484866, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 860);