Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C17 ⋊ C4 |
| Sylow | C17 ⋊ #1508 |
294 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 64 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=e,b^2=f,c^2=g,d^2=g,b^a=bd,d^a=df,h^a=h^13,c^b=cf,d^b=dg,e^b=efg,h^c=h^16,h^e=h^16112 conjugacy classes — view the full character table.
| maximal subgroup of | #17952610, #17952611, #17952614, … |
| maximal normal subgroup of | #17952610, #17952611, #17952614, … |
| maximal quotient of | #17949687, #17949696, #17949724, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19909);