Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×C4⋊#3866 |
| unambiguous semidirect product | D37⋊(C2×C4⋊C4) |
| Fitting | C22×C4×C37 ⋊ C4 |
| Sylow | C37 ⋊ C22×C4⋊C4 |
418 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | #18009773, #18009774, #18009776, … |
| maximal normal subgroup of | #18009773, #18009774, #18009776, … |
| maximal quotient of | C22×(C2×#3866)⋊C4, C2×C4×C4⋊#3866, C2×#14558475, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1611);