Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C17 ⋊ #2987 |
314 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 144 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=e,c^2=e,f^2=g,b^a=be,c^a=cg,d^a=de,h^a=h^13,c^b=ceg,d^b=dg,h^c=h^16,h^d=h^16,h^f=h^1694 conjugacy classes — view the full character table.
| maximal subgroup of | #17955360, #17955361, #17955362, … |
| maximal normal subgroup of | #17955360, #17955361, #17955362, … |
| maximal quotient of | #17968959, #17968969, #17969136, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21424);