Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C22×C4 |
| unambiguous semidirect product | (C2×#3633)⋊C8 |
| Fitting | C2×C8×C17 ⋊ C8 |
| Sylow | C17 ⋊ #1273 |
212 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 85 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=d,b^2=e,d^2=f,e^2=g,b^a=bc,h^a=h^9,h^d=h^13,h^f=h^16112 conjugacy classes — view the full character table.
| maximal subgroup of | #17981161, #17981162, #17981169, … |
| maximal normal subgroup of | #17981161, #17981162, #17981169, … |
| maximal quotient of | #17981066, #17981067, #17981068, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21512);