Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C17×#123 ⋊ C2 |
| Sylow | C17 ⋊ #2534 |
800 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 161 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|b^2=eg,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^16,h^c=h^16262 conjugacy classes — view the full character table.
| maximal subgroup of | #16952613, #16952626, #17087713, … |
| maximal normal subgroup of | #16952613, #16952626, #17087713, … |
| maximal quotient of | #16956548, #16957042, #16957099, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 9399);