Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C17 ⋊ C8×D4 |
134 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 56 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^a=g^4,g^c=g^13,g^e=g^1680 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11763836, D4×#63242, #14545498, … |
| maximal normal subgroup of | C2×#11763836, D4×#63242, #14545498, … |
| maximal quotient of | #14544364, #14544367, #14544368, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1576);