Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×Q16×C17 ⋊ C4 |
| Sylow | C17 ⋊ #2957 |
452 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 158 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=f,c^2=f,e^2=g,f^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^4,e^b=eg,h^b=h^16,d^c=dg,h^c=h^13,h^f=h^16100 conjugacy classes — view the full character table.
| maximal subgroup of | #17961739, #17961753, #17961885, … |
| maximal normal subgroup of | #17961739, #17961753, #17961885, … |
| maximal quotient of | #17966642, #17966646, #17966649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21290);