Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | #120×#595 |
| Fitting | C17×#120 ⋊ C4 |
| Sylow | C17 ⋊ C4×#120 |
1224 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 136 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | AΣL(1,𝔽16)×#595, B(4,𝔽2)×#595, C2×#120×#595, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×#595, B(4,𝔽2)×#595, C2×#120×#595, … |
| maximal quotient of | #386×#595, #385×#595, #379×#595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20973);