Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C239 ⋊ #441 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15296 |
Polycyclic presentation:
2^6,239|a^2=e,b^2=f,c^2=e,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^238,d^b=df,g^c=g^2381688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44486440, #44486442 |
| maximal normal subgroup of | #44486440, #44486442 |
| maximal quotient of | #44483367, #44483420, #44483457, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 656);