Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C17×#462 ⋊ C2 |
| Sylow | C17 ⋊ D4×Q16 |
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,d^b=de,e^b=eg,h^c=h^16,e^d=eg,h^d=h^16187 conjugacy classes — view the full character table.
| maximal subgroup of | #17023756, #17023759, #17023764, … |
| maximal normal subgroup of | #17023756, #17023759, #17023764, … |
| maximal quotient of | #17024508, #17024518, #17024523, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 16257);