Finite Group DatabasebetaFinite Group Databasebeta| order | 17984 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C281 ⋊ #387 |
154 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 17984 |
Polycyclic presentation:
2^6,281|a^2=f,b^2=f,c^2=d,b^a=bd,c^a=ce,g^c=g^2802828 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #387×D281, C2×#31823344, #49097739, … |
| maximal normal subgroup of | #387×D281, C2×#31823344, #49097739, … |
| maximal quotient of | #49093527, #49093534, #49093535, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17984, 430);