Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4 |
| direct product | C22×C4⋊C4×#6157 |
| Fitting | C22×C4⋊C4×C53 ⋊ C4 |
| Sylow | C53 ⋊ C22×C4×C4⋊C4 |
5758 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1114095);