Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C17×C22⋊C8 ⋊ C2 |
| Sylow | C17 ⋊ C8×D4 |
134 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^6,17|a^2=e,c^2=e,e^2=f,b^a=bd,g^c=g^16200 conjugacy classes — view the full character table.
| maximal subgroup of | C8×D4×D17, C2×#11762872, #14537474, … |
| maximal normal subgroup of | C8×D4×D17, C2×#11762872, #14537474, … |
| maximal quotient of | #14527576, #14527581, #14527587, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 612);