Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C17 ⋊ #1694 |
152 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 55 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=g,b^2=df,c^2=g,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,c^b=cf,e^c=eg,h^c=h^16199 conjugacy classes — view the full character table.
| maximal subgroup of | #16948255, #16948257, #16948262, … |
| maximal normal subgroup of | #16948255, #16948257, #16948262, … |
| maximal quotient of | #16927420, #16930543, #16932725, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 4025);