Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C27 |
| direct product | C22×C22⋊#3633 |
| unambiguous semidirect product | (C2×#3633)⋊C23 |
| Fitting | C24×C17 ⋊ C8 |
| Sylow | C17 ⋊ C22×C22⋊C8 |
1072 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 287 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14545793, #17981581, C2×#14545795, … |
| maximal normal subgroup of | C2×#14545793, #17981581, C2×#14545795, … |
| maximal quotient of | C22×#11763894, C22×#11763895, C2×#14545896, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21746);