Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×C4×C17 ⋊ C8 |
| Sylow | C17 ⋊ #1817 |
380 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=f,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^9,h^f=h^13,h^g=h^1688 conjugacy classes — view the full character table.
| maximal subgroup of | #17981071, #17981075, #17981087, … |
| maximal normal subgroup of | #17981071, #17981075, #17981087, … |
| maximal quotient of | #17981668, #17981669, #17981670, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21651);