Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C239 ⋊ #451 |
148 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|a^2=f,b^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^238,d^b=df2399 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44483503, #44483504, #44483508, … |
| maximal normal subgroup of | #44483503, #44483504, #44483508, … |
| maximal quotient of | #44483505, #44483522, #44483573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 705);