Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C17×#104 ⋊ C4 |
| Sylow | C17 ⋊ #1860 |
286 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 68 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,b^2=f,c^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^4,d^b=dg,h^b=h^13,e^c=eg,h^f=h^1688 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14544744, #17969810, #17969811, … |
| maximal normal subgroup of | C2×#14544744, #17969810, #17969811, … |
| maximal quotient of | #17953890, #17953891, #17953892, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20470);