Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C239 ⋊ #440 |
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|a^2=e,c^2=e,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^238,d^b=df2402 conjugacy classes. The character table is too large to display.
| maximal quotient of | #44483360, #44483405, #44483424, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 649);