Finite Group DatabasebetaFinite Group Databasebeta| order | 16064 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×(C2×D251)⋊C4 |
| Fitting | C23×C4×C251 ⋊ C2 |
| Sylow | C251 ⋊ C22×C22⋊C4 |
674 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8032 |
4040 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C2×D251)⋊#95, #44548601, #44548603, … |
| maximal normal subgroup of | (C2×D251)⋊#95, #44548601, #44548603, … |
| maximal quotient of | C22×C251⋊#95, C2×C4×(C2×D251)⋊C4, C2×#30631542, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16064, 996);