Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C239 ⋊ #504 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|a^2=d,d^2=e,e^2=f,g^a=g^238,c^b=cf2420 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44486382, #44486385, #44486387, … |
| maximal normal subgroup of | #44486382, #44486385, #44486387, … |
| maximal quotient of | #44486145, #44486162, #44486307, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 966);