Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#11762997 |
| Fitting | C2×C17×#99 ⋊ C2 |
| Sylow | C17 ⋊ C2×B(4,𝔽2) |
1018 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 1018 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) = 272 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #16951583, #16951585, #16951597, … |
| maximal normal subgroup of | #16951583, #16951585, #16951597, … |
| maximal quotient of | C2×#14527703, C2×#14527704, C2×#14527737, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 13895);