Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C17 ⋊ #1704 |
140 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 51 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=f,b^2=dfg,c^2=g,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^16,c^b=cf,h^b=h^16,e^c=eg175 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#1704, C2×#14528368, #17017000, … |
| maximal normal subgroup of | D17×#1704, C2×#14528368, #17017000, … |
| maximal quotient of | #16927441, #16930528, #16930552, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 4094);