Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C239 ⋊ #397 |
170 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 57 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=d,b^a=bd,c^a=ce,g^a=g^238,c^b=cf2402 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #397×D239, C2×#29504700, #44487790, … |
| maximal normal subgroup of | #397×D239, C2×#29504700, #44487790, … |
| maximal quotient of | #44482791, #44482795, #44482797, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 477);