Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C8×C239 ⋊ C2 |
| Sylow | C239 ⋊ #461 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|a^2=f,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^238,e^c=ef,g^c=g^2382399 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44483728, #44483730, #44483749, … |
| maximal normal subgroup of | #44483728, #44483730, #44483749, … |
| maximal quotient of | #44483924, #44483938, #44483948, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 755);