Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C22×C4⋊C4×C17 ⋊ C2 |
| Sylow | C17 ⋊ #2623 |
526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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=e,b^2=f,b^a=be,c^a=cf,c^b=cg,d^c=de,h^c=h^16352 conjugacy classes — view the full character table.
| maximal subgroup of | #17007568, #17007572, #17007579, … |
| maximal normal subgroup of | #17007568, #17007572, #17007579, … |
| maximal quotient of | #16960685, #16960706, #16960741, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 10290);