Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C17×H(5,𝔽2) ⋊ C4 |
| Sylow | C17 ⋊ #1792 |
620 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 136 |
Polycyclic presentation:
2^7,17|a^2=f,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^13,d^b=dg,e^b=eg,d^c=dg,h^f=h^16100 conjugacy classes — view the full character table.
| maximal subgroup of | #17961924, #17961925, #17961926, … |
| maximal normal subgroup of | #17961924, #17961925, #17961926, … |
| maximal quotient of | #17952490, #17952491, #17952492, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20356);