Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C17 ⋊ C2×#350 |
224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 69 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=e,d^2=g,e^2=f,f^2=g,b^a=bd,h^a=h^9,d^b=dg,e^b=eg,h^c=h^16,h^e=h^13,h^f=h^1676 conjugacy classes — view the full character table.
| maximal subgroup of | #595⋊#350, #17982440, #17982454, … |
| maximal normal subgroup of | #595⋊#350, #17982440, #17982454, … |
| maximal quotient of | #17981870, #17981875, #17981912, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21690);