Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C239 ⋊ #330 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15296 |
Polycyclic presentation:
2^6,239|a^2=d,b^2=e,c^2=f,d^2=e,b^a=bc,c^a=ce,g^a=g^238,c^b=cf,d^b=def1685 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #330×D239, C2×#29504514, #44483135, … |
| maximal normal subgroup of | #330×D239, C2×#29504514, #44483135, … |
| maximal quotient of | #44482371, #44482429, C2×#29504514 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 291);