Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C239 ⋊ #443 |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3824 |
Polycyclic presentation:
2^6,239|a^2=e,c^2=e,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^238,d^b=df,g^c=g^2381694 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44486426, #44486429, #44486431, … |
| maximal normal subgroup of | #44486426, #44486429, #44486431, … |
| maximal quotient of | D8×C239⋊C8, SD16×C239⋊C8, Q16×C239⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 666);