Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C8×Q8×C17 ⋊ C2 |
| Sylow | C17 ⋊ #2991 |
394 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 179 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,d^2=e,f^2=g,b^a=be,c^a=cg,d^a=de,c^b=ceg,h^b=h^16,h^c=h^16,h^d=h^16370 conjugacy classes — view the full character table.
| maximal subgroup of | #17005525, #17005531, #17005536, … |
| maximal normal subgroup of | #17005525, #17005531, #17005536, … |
| maximal quotient of | #17033163, #17033349, #17033386, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 13641);