Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C17×#123 ⋊ C2 |
| Sylow | C17 ⋊ #2697 |
680 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 137 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|a^2=ef,b^2=ef,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^c=h^16256 conjugacy classes — view the full character table.
| maximal subgroup of | #16953266, #16953268, #16953743, … |
| maximal normal subgroup of | #16953266, #16953268, #16953743, … |
| maximal quotient of | #16961612, #16961723, #16961854, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 11069);