Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C239 ⋊ #381 |
218 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|a^2=f,c^2=d,b^a=bd,c^a=ce,g^a=g^2383836 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44482401, #44482402, #44482457, … |
| maximal normal subgroup of | #44482401, #44482402, #44482457, … |
| maximal quotient of | #44482771, #44482775, #44482797, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 412);