Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C17 ⋊ #2108 |
184 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=e,d^2=f,f^2=g,h^a=h^16,c^b=cg400 conjugacy classes — view the full character table.
| maximal subgroup of | #16945980, #16945984, #16949157, … |
| maximal normal subgroup of | #16945980, #16945984, #16949157, … |
| maximal quotient of | #16943306, #16943313, M16×#63214, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 6107);