Finite Group DatabasebetaFinite Group Databasebeta| order | 16976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#16862558 |
| unambiguous semidirect product | (C2×#16862558)⋊C2 |
| Fitting | C22×C1061 ⋊ C4 |
| Sylow | C1061 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4244 |
Polycyclic presentation:
2^4,1061|a^2=d,b^a=bc,e^a=e^958,e^d=e^10601070 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46800688, #46800689, C2×C22⋊#16862558, … |
| maximal normal subgroup of | #46800688, #46800689, C2×C22⋊#16862558, … |
| maximal quotient of | (C2×#16862558)⋊C4, C22⋊#22555123, #46800687, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16976, 45);