Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×D4×C17 ⋊ C4 |
| Sylow | C17 ⋊ #1806 |
312 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 80 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:
2^7,17|a^2=f,b^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^13,e^c=eg,h^f=h^16118 conjugacy classes — view the full character table.
| maximal subgroup of | #17952810, #17952813, #17952814, … |
| maximal normal subgroup of | #17952810, #17952813, #17952814, … |
| maximal quotient of | #17953150, #17953155, #17953160, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20382);