Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #117×C239 ⋊ C2 |
| Sylow | C239 ⋊ #518 |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3824 |
Polycyclic presentation:
2^6,239|a^2=f,b^a=be,d^a=de,c^b=ce,g^b=g^238,g^c=g^2382414 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44484658, #44484756, #44484759, … |
| maximal normal subgroup of | #44484658, #44484756, #44484759, … |
| maximal quotient of | #44486900, #44486904, #44486908, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 1023);