Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ C8×Q16 |
164 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^7,17|a^2=e,b^2=f,c^2=ef,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^4,d^b=df,h^c=h^13,h^e=h^16112 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14544371, Q16×#63242, #17966591, … |
| maximal normal subgroup of | C2×#14544371, Q16×#63242, #17966591, … |
| maximal quotient of | #103×#3624, #17951984, #17952348, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20097);