Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C239 ⋊ #341 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|a^2=d,b^2=e,c^2=f,d^2=f,e^2=f,b^a=bc,c^a=cf,e^a=ef,g^a=g^2383836 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44482563, #44482564, #44482566, … |
| maximal normal subgroup of | #44482563, #44482564, #44482566, … |
| maximal quotient of | #44482383, #44482385, #44482410, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 314);