Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | H(5,𝔽2)×#595 |
| Fitting | C17×H(5,𝔽2) ⋊ C4 |
| Sylow | C17 ⋊ C4×H(5,𝔽2) |
1660 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 1660 conjugacy classes of subgroups — too many to draw. Only its 754 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 136 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #453×#595, #455×#595, #17971218, … |
| maximal normal subgroup of | #453×#595, #455×#595, #17971218, … |
| maximal quotient of | #518×#595, #520×#595, #534×#595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21491);