Finite Group DatabasebetaFinite Group Databasebeta| order | 24224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊#15690044 |
| unambiguous semidirect product | D757⋊(C4⋊C4) |
| Fitting | C2×C4×C757 ⋊ C4 |
| Sylow | C757 ⋊ C2×C4⋊C4 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6056 |
1532 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24224, 224);