Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×#3866 |
| unambiguous semidirect product | D37⋊(C4×D4) |
| Fitting | C2×D4×C37 ⋊ C4 |
| Sylow | C37 ⋊ C2×C4×D4 |
426 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 296 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | #99×#3866, #100×#3866, #102×#3866, … |
| maximal normal subgroup of | #99×#3866, #100×#3866, #102×#3866, … |
| maximal quotient of | C2×C22⋊C4×#3866, C2×C4⋊C4×#3866, C4×D4×#3866, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1613);