Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C239 ⋊ #389 |
170 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 15296 |
Polycyclic presentation:
2^6,239|a^2=f,b^2=f,c^2=e,b^a=bd,c^a=ce,g^b=g^2382408 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44484792, #44484793, #44484799, … |
| maximal normal subgroup of | #44484792, #44484793, #44484799, … |
| maximal quotient of | #44482777, #44482779, #44482800, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 445);