Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C22×C42×C17 ⋊ C2 |
| Sylow | C17 ⋊ #1437 |
828 conjugacy classes of subgroups; only the 241 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 241 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=f,b^2=g,c^2=ef,b^a=bd,c^a=ce,h^a=h^16568 conjugacy classes — view the full character table.
| maximal subgroup of | #16925836, D17×#1437, C2×#14527022, … |
| maximal normal subgroup of | #16925836, D17×#1437, C2×#14527022, … |
| maximal quotient of | #16922244, #16922245, #16922247, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2748);