Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C8×C271 ⋊ C2 |
| Sylow | C271 ⋊ #436 |
122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 122 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) = 8672 |
Polycyclic presentation:
2^6,271|a^2=e,c^2=e,e^2=f,b^a=bd,c^a=cf,c^b=cf,g^c=g^2702728 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #436×D271, C2×#31773972, #46845062, … |
| maximal normal subgroup of | #436×D271, C2×#31773972, #46845062, … |
| maximal quotient of | #46835246, #46835251, #46835257, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 624);